Are these practice questions for Surface Areas And Volumes based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 10 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Surface Areas And Volumes free?

Yes. Every chapter includes free practice questions for Class 10 students to get you started.

What types of questions are included?

The practice set for Surface Areas And Volumes mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Surface Areas And Volumes for full coverage.

How many practice questions are there for Surface Areas And Volumes?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Surface Areas And Volumes Class 10 Mathematics Practice Questions with Answers

easy

From a solid cylinder of height 10 cm and base radius 4 cm, a conical cavity of the same height and same base radius is hollowed out. Determine the volume of the remaining solid.

Try solving it in your notebook first, then check the solution.

easy

A company manufactures two types of containers. Container A is a cylinder with a radius of 7 cm and a height of 14 cm. Container B is a cube with an edge of 12 cm. Justify which container is a more "efficient" use of material by comparing their volume-to-surface-area ratios. (Use

\pi = \frac{22}{7}

)

Try solving it in your notebook first, then check the solution.

easy

Calculate the volume of a solid formed by a cone of radius 3 cm and height 4 cm, mounted on a hemisphere of radius 3 cm.

Try solving it in your notebook first, then check the solution.

easy

List the formulas required to calculate the total surface area of canvas used for a tent which is in the shape of a cylinder surmounted by a conical top. (Assume the base is not covered with canvas).

Try solving it in your notebook first, then check the solution.

easy

Explain why, when finding the surface area of a new solid formed by joining two identical cubes end-to-end, we do not simply add their individual total surface areas.

Try solving it in your notebook first, then check the solution.

easy

A student argues that to find the surface area of a toy made of a cone mounted on a hemisphere, one must add the Total Surface Area (TSA) of the cone and the TSA of the hemisphere. Critique this argument.

Try solving it in your notebook first, then check the solution.

easy

To double the volume of a solid sphere, a student proposes doubling its radius. Justify whether this proposal is correct or incorrect.

Try solving it in your notebook first, then check the solution.

easy

State the formula for the volume of a hemisphere with radius '

r

'.

Try solving it in your notebook first, then check the solution.

easy

Define the Total Surface Area (TSA) of a solid object.

Try solving it in your notebook first, then check the solution.

easy

State the formula for the Curved Surface Area (CSA) of a cylinder with radius '

r

' and height '

h

'.

Try solving it in your notebook first, then check the solution.

easy

List the two basic solids that are combined to form a medicine capsule as shown in the chapter.

Try solving it in your notebook first, then check the solution.

medium

A tent is in the shape of a cylinder surmounted by a cone. The height of the cylindrical part is 3 m and its diameter is 14 m. The slant height of the conical top is 9 m. Calculate the area of the canvas required for the tent, and find the cost if the canvas costs ₹450 per

\text{m}^2

.

Try solving it in your notebook first, then check the solution.

medium

Identify the component areas needed to calculate the total surface area of a bird-bath shaped like a cylinder with a hemispherical depression at one end.

Try solving it in your notebook first, then check the solution.

medium

Explain the difference between the 'apparent capacity' and 'actual capacity' of a cylindrical glass that has a hemispherical raised portion at the bottom.

Try solving it in your notebook first, then check the solution.

medium

A wooden article is created by scooping out a hemisphere from each end of a solid cylinder. The height of the cylinder is 15 cm and the radius of its base is 4 cm. Calculate the total surface area of the article.

Try solving it in your notebook first, then check the solution.

medium

Summarize the procedure to find the volume of air in a shed shaped like a cuboid surmounted by a half-cylinder, after accounting for machinery and workers inside.

Try solving it in your notebook first, then check the solution.

medium

Create a problem involving a composite solid made from a cylinder and at least one other shape, where the total volume is exactly

300\pi \text{ cm}^3

. Provide the dimensions you chose and verify the volume.

Try solving it in your notebook first, then check the solution.

medium

Formulate a single algebraic expression for the surface area of a solid composed of a cube of edge '

a

' with a hemispherical depression of diameter '

a

' carved out from one of its faces.

Try solving it in your notebook first, then check the solution.

medium

A solid is formed by mounting a cone on a hemisphere of the same radius. Explain which surface areas are included in the total surface area of this new solid.

Try solving it in your notebook first, then check the solution.

medium

Describe the steps to find the height of the conical part of a toy that is composed of a cone mounted on a hemisphere, given the total height of the toy and the radius of the hemisphere.

Try solving it in your notebook first, then check the solution.

medium

A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter the hemisphere can have? Calculate the surface area of the solid with this hemisphere.

Try solving it in your notebook first, then check the solution.

medium

Design a storage silo in the shape of a cylinder surmounted by a cone. The radius of the base is to be 3 m. The total height of the silo must be 13 m. The cost of material for the cylindrical part is ₹100 per m² and for the conical part is ₹250 per m² (due to complexity). Propose a design by choosing a height for the cylindrical part, and then justify your design by calculating the total material cost. Propose a different height for the cylinder and evaluate if it would be cheaper or more expensive.

Try solving it in your notebook first, then check the solution.

medium

A juice glass is cylindrical with an inner diameter of 6 cm. The bottom of the glass has a hemispherical raised portion that reduces its capacity. If the height of the glass is 12 cm, calculate the actual capacity of the glass. (Use

\pi = 3.14

)

Try solving it in your notebook first, then check the solution.

medium

Two cubes, each with a volume of 125 cm³, are joined end to end. Calculate the surface area of the resulting cuboid.

Try solving it in your notebook first, then check the solution.

medium

A model is shaped like a cylinder with two cones attached to its ends. The total length of the model is 15 cm and its diameter is 4 cm. If each cone has a height of 3 cm, analyze the dimensions and find the volume of the model.

Try solving it in your notebook first, then check the solution.

medium

You have a fixed amount of metal sheet to create a closed cylindrical container. Evaluate which of these two conflicting goals is the practical objective in engineering design: maximizing the container's volume or maximizing its surface area.

Try solving it in your notebook first, then check the solution.

medium

Describe the method to find the volume of a solid formed by joining two basic solids. Contrast this with the method for finding the surface area of the same combined solid. Use the example of a toy shaped like a cone on a hemisphere to illustrate.

Try solving it in your notebook first, then check the solution.

medium

A solid toy is a cylinder of height 8 cm and radius 3 cm, with a conical cavity of the same height and radius hollowed out from it. Another toy is a solid hemisphere of radius 4.1 cm. Evaluate which toy is heavier, assuming both are made of the same wood with uniform density. (Use

\pi = 3.14

)

Try solving it in your notebook first, then check the solution.

medium

Explain in detail the general principle for finding the surface area of a combination of solids. Use the example of a decorative block made of a cube with a hemisphere fixed on top to illustrate your explanation. Specifically, mention why an area is subtracted.

Try solving it in your notebook first, then check the solution.

medium

Calculate the surface area of a toy which is in the form of a cone of radius 6 cm mounted on a hemisphere of the same radius. The total height of the toy is 14 cm. (Use

\pi = \frac{22}{7}

)

Try solving it in your notebook first, then check the solution.

medium

An artist wants to create a solid sculpture by joining two identical solid cones at their bases. The resulting solid is a bicone. The artist claims that the surface area of this new solid is double the total surface area of a single cone. Justify whether this claim is correct.

Try solving it in your notebook first, then check the solution.

medium

A solid iron pole consists of a cylinder of height 150 cm and base diameter 20 cm, surmounted by another cylinder of height 50 cm and radius 6 cm. Calculate the volume of the pole. (Use

\pi = 3.14

)

Try solving it in your notebook first, then check the solution.

medium

A solid is composed of a cylinder with hemispherical ends. If the total length of the solid is 28 cm and the diameter of the cylinder is 10 cm, calculate its volume. (Use

\pi = \frac{22}{7}

)

Try solving it in your notebook first, then check the solution.

medium

Calculate the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.

Try solving it in your notebook first, then check the solution.

medium

To find the volume of wood in a cubical block of side 10 cm with a hemispherical scoop of diameter 6 cm removed, a student calculates: Volume = (Volume of Cube) + (Volume of Hemisphere). Critique the student's formula and provide the correct calculation. (Use

\pi = 3.14

)

Try solving it in your notebook first, then check the solution.

hard

Summarize how to calculate the area to be painted for a wooden toy rocket shaped like a cone mounted on a cylinder, where the base of the cone is wider than the base of the cylinder. List all the individual areas that must be calculated for both the conical (orange) and cylindrical (yellow) portions as described in the source text.

Try solving it in your notebook first, then check the solution.

hard

A cone of height 24 cm has a curved surface area of

550 \text{ cm}^2

. Calculate the radius of its base. (Use

\pi = \frac{22}{7}

)

Try solving it in your notebook first, then check the solution.

hard

From a solid wooden cube of side 14 cm, a hemisphere of the largest possible diameter is carved out from one face. Calculate the surface area of the remaining solid.

Try solving it in your notebook first, then check the solution.

hard

A company wants to create a bird bath from a single solid block of wood shaped like a cylinder with height 50 cm and radius 20 cm. The design requires scooping out a hemisphere from the top face. To save material, the company wants the volume of the wood scooped out to be exactly 25% of the original cylinder's volume. Create the specifications for this bird bath by determining the required radius of the hemispherical depression. Justify whether such a design is physically possible within the dimensions of the block.

Try solving it in your notebook first, then check the solution.

hard

Propose a modification to the shape of a standard right circular cylinder that would increase its volume without changing its height or the area of its curved surface.

Try solving it in your notebook first, then check the solution.

hard

A tent is shaped like a cylinder surmounted by a cone. The radius of the base is

r

. The height of the cylinder is

h_1

and the height of the cone is

h_2

. Formulate a single expression for the total cost of the canvas required at a rate of ₹C per m², assuming the floor is not covered.

Try solving it in your notebook first, then check the solution.

hard

Given a solid cylinder from which a conical cavity of the same height and same base radius is hollowed out, describe which surfaces constitute the total surface area of the remaining solid.

Try solving it in your notebook first, then check the solution.

hard

A cylindrical container with radius 6 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and radius 3 cm, having a hemispherical top. Evaluate how many such cones can be filled with ice cream.

Try solving it in your notebook first, then check the solution.

hard

A rocket is shaped like a cylinder of radius

R

and height

H

, surmounted by a cone of the same radius

R

and height

h

. Formulate a general expression for the ratio of the rocket's total volume to its total surface area (excluding the base). Then, evaluate this "efficiency ratio" for a rocket where

R=2

m,

H=10

m, and

h=3

m.

Try solving it in your notebook first, then check the solution.

Surface Areas And VolumesClass 10 Mathematics Practice Questions