Question 1

Q1: Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm . Find its curved surface area.

Accepted Answer

Given: Diameter of the base of a cone, $d = 10.5 	ext{ cm}$ Slant height of the cone, $l = 10 	ext{ cm}$ To Find: Curved surface area of the cone. Solution: First, we find the radius of the base of the cone. Radius, $r = \frac{	ext{Diameter}}{2} = \frac{10.5}{2} = 5.25 	ext{ cm}$ Formula: The cu...

Question 2

Q2: Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m .

Accepted Answer

Given: Slant height of the cone, $l = 21 	ext{ m}$ Diameter of the base of the cone, $d = 24 	ext{ m}$ To Find: Total surface area of the cone. Solution: First, we find the radius of the base of the cone. Radius, $r = \frac{	ext{Diameter}}{2} = \frac{24}{2} = 12 	ext{ m}$ Formula: The total surf...

Question 3

Q3: Curved surface area of a cone is $308 \mathrm{~cm}^{2}$ and its slant height is 14 cm . Find (i) radius of the base and (ii) total surface area of the...

Accepted Answer

Given: Curved surface area (CSA) of a cone = $308 	ext{ cm}^2$ Slant height of the cone, $l = 14 	ext{ cm}$ To Find: (i) Radius of the base ($r$) (ii) Total surface area (TSA) of the cone Solution: (i) Finding the radius of the base: Formula: $$ 	ext{CSA} = \pi r l $$ Substituting the given value...

Question 4

Q4: A conical tent is 10 m high and the radius of its base is 24 m . Find (i) slant height of the tent. (ii) cost of the canvas required to make the tent,...

Accepted Answer

Given: Height of the conical tent, $h = 10 	ext{ m}$ Radius of the base of the tent, $r = 24 	ext{ m}$ Cost of canvas = ₹ 70 per $	ext{m}^2$ To Find: (i) Slant height of the tent ($l$) (ii) Cost of the canvas required Solution: (i) Finding the slant height of the tent: Formula: The relationship b...

Question 5

Q5: What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m ? Assume that the extra length of material t...

Accepted Answer

Given: Height of the conical tent, $h = 8 	ext{ m}$ Base radius of the tent, $r = 6 	ext{ m}$ Width of the tarpaulin = $3 	ext{ m}$ Extra length for stitching and wastage = $20 	ext{ cm} = 0.2 	ext{ m}$ Value of $\pi = 3.14$ To Find: The total length of tarpaulin required. Solution: First, we n...

Question 6

Q6: The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of...

Accepted Answer

Given: Slant height of the conical tomb, $l = 25 	ext{ m}$ Base diameter of the tomb, $d = 14 	ext{ m}$ Rate of white-washing = ₹ 210 per $100 	ext{ m}^2$ To Find: The cost of white-washing the curved surface of the tomb. Solution: First, we find the radius of the base. Radius, $r = \frac{	ext{D...

Question 7

Q7: A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm . Find the area of the sheet required to make 10 such caps.

Accepted Answer

Given: Base radius of the conical cap, $r = 7 	ext{ cm}$ Height of the conical cap, $h = 24 	ext{ cm}$ Number of caps to be made = 10 To Find: The total area of the sheet required to make 10 caps. Solution: The area of the sheet required for one cap is equal to its curved surface area (CSA). Step...

Question 8

Q8: A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40...

Accepted Answer

Given: Number of hollow cones = 50 Base diameter of each cone, $d = 40 	ext{ cm}$ Height of each cone, $h = 1 	ext{ m}$ Cost of painting = ₹ 12 per $	ext{m}^2$ Values to use: $\pi = 3.14$ and $\sqrt{1.04} = 1.02$ To Find: The total cost of painting all 50 cones. Solution: Since the cost is given...

Question 9

Q1: Find the surface area of a sphere of radius: (i) 10.5 cm (ii) 5.6 cm (iii) 14 cm

Accepted Answer

To Find: The surface area of a sphere for the given radii. Formula: The surface area (SA) of a sphere is given by: $$ 	ext{SA} = 4 \pi r^2 $$ where $r$ is the radius of the sphere. We use $\pi = \frac{22}{7}$. (i) Radius, $r = 10.5 	ext{ cm}$ $$ 	ext{SA} = 4 	imes \frac{22}{7} 	imes (10.5)^2 $$...

Question 10

Q2: Find the surface area of a sphere of diameter: (i) 14 cm (ii) 21 cm (iii) 3.5 m

Accepted Answer

To Find: The surface area of a sphere for the given diameters. Formula: The surface area (SA) of a sphere is given by: $$ 	ext{SA} = 4 \pi r^2 $$ where $r$ is the radius. First, we must find the radius from the diameter using $r = d/2$. We use $\pi = \frac{22}{7}$. (i) Diameter, $d = 14 	ext{ cm}$...

Question 11

Q3: Find the total surface area of a hemisphere of radius 10 cm . (Use $\pi=3.14$ )

Accepted Answer

Given: Radius of the hemisphere, $r = 10 	ext{ cm}$ Value of $\pi = 3.14$ To Find: The total surface area of the hemisphere. Formula: The total surface area (TSA) of a hemisphere is the sum of its curved surface area ($2\pi r^2$) and the area of its circular base ($\pi r^2$). $$ 	ext{TSA} = 3 \pi...

Question 12

Q4: The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the t...

Accepted Answer

Given: Initial radius of the balloon, $r_1 = 7 	ext{ cm}$ Final radius of the balloon, $r_2 = 14 	ext{ cm}$ To Find: The ratio of the surface areas of the balloon in the two cases. Solution: Let the initial surface area be $S_1$ and the final surface area be $S_2$. Formula: The surface area (SA) o...

Question 13

Q5: A hemispherical bowl made of brass has inner diameter 10.5 cm . Find the cost of tin-plating it on the inside at the rate of ₹ 16 per $100 \mathrm{~cm...

Accepted Answer

Given: Inner diameter of the hemispherical bowl, $d = 10.5 	ext{ cm}$ Rate of tin-plating = ₹ 16 per $100 	ext{ cm}^2$ To Find: The cost of tin-plating the inside of the bowl. Solution: First, we find the inner radius of the bowl. Inner radius, $r = \frac{d}{2} = \frac{10.5}{2} = 5.25 	ext{ cm}$...

Question 14

Q6: Find the radius of a sphere whose surface area is $154 \mathrm{~cm}^{2}$.

Accepted Answer

Given: Surface area (SA) of the sphere = $154 	ext{ cm}^2$ To Find: The radius ($r$) of the sphere. Formula: The surface area of a sphere is given by: $$ 	ext{SA} = 4 \pi r^2 $$ Solution: Substitute the given surface area into the formula: $$ 154 = 4 	imes \frac{22}{7} 	imes r^2 $$ $$ 154 = \fra...

Question 15

Q7: The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Accepted Answer

Given: The diameter of the moon is approximately one fourth of the diameter of the earth. To Find: The ratio of their surface areas (Moon's SA : Earth's SA). Solution: Let $D_e$ be the diameter of the Earth and $D_m$ be the diameter of the Moon. Let $r_e$ be the radius of the Earth and $r_m$ be the...

Question 16

Q8: A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm . Find the outer curved surface area of the bowl.

Accepted Answer

Given: Inner radius of the hemispherical bowl, $r_{inner} = 5 	ext{ cm}$ Thickness of the steel = $0.25 	ext{ cm}$ To Find: The outer curved surface area of the bowl. Solution: To find the outer curved surface area, we first need to determine the outer radius of the bowl. Outer radius, $r_{outer}...

Question 17

Q9: A right circular cylinder just encloses a sphere of radius $r$. Find (i) surface area of the sphere, (ii) curved surface area of the cylinder, (iii) r...

Accepted Answer

Given: A right circular cylinder just encloses a sphere of radius $r$. This means: - The radius of the cylinder's base is equal to the radius of the sphere, so cylinder radius = $r$. - The height of the cylinder is equal to the diameter of the sphere, so cylinder height $h = 2r$. To Find: (i) Surfac...

Question 18

Q1: Find the volume of the right circular cone with (i) radius 6 cm , height 7 cm (ii) radius 3.5 cm , height 12 cm

Accepted Answer

To Find: The volume of the right circular cone for the given dimensions. Formula: The volume (V) of a cone is given by: $$ V = \frac{1}{3} \pi r^2 h $$ where $r$ is the radius and $h$ is the height. We use $\pi = \frac{22}{7}$. (i) Radius $r = 6 	ext{ cm}$, height $h = 7 	ext{ cm}$ $$ V = \frac{1}...

Question 19

Q2: Find the capacity in litres of a conical vessel with (i) radius 7 cm , slant height 25 cm (ii) height 12 cm , slant height 13 cm

Accepted Answer

To Find: The capacity in litres of the conical vessel for the given dimensions. (Note: $1000 	ext{ cm}^3 = 1 	ext{ litre}$) Formula: Volume of a cone, $V = \frac{1}{3} \pi r^2 h$. Relationship between $r, h, l$: $l^2 = r^2 + h^2$. (i) Radius $r = 7 	ext{ cm}$, slant height $l = 25 	ext{ cm}$ Fir...

Question 20

Q3: The height of a cone is 15 cm . If its volume is $1570 \mathrm{~cm}^{3}$, find the radius of the base. (Use $\pi=3.14$ )

Accepted Answer

Given: Height of the cone, $h = 15 	ext{ cm}$ Volume of the cone, $V = 1570 	ext{ cm}^3$ Value of $\pi = 3.14$ To Find: The radius of the base of the cone ($r$). Formula: The volume of a cone is given by: $$ V = \frac{1}{3} \pi r^2 h $$ Solution: Substitute the given values into the formula: $$ 15...

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