Key Points

The slant height ($l$), height ($h$), and radius ($r$) of a right circular cone are related by the Pythagorean theorem. The formula is $l^2 = r^2 + h^2$, which means $l = \sqrt{r^2 + h^2}$.

The curved surface area (CSA) of a right circular cone is the area of its slanted surface. It is calculated using the formula $CSA = \pi r l$, where $r$ is the radius of the base and $l$ is the slant height.

The total surface area (TSA) of a cone is the sum of its curved area and the area of its circular base. The formula is $TSA = \pi r l + \pi r^2$, which simplifies to $TSA = \pi r(l + r)$.

The volume of a right circular cone is given by the formula $V = \frac{1}{3} \pi r^2 h$. Here, $r$ is the radius of the base and $h$ is the perpendicular height of the cone.

A sphere has a single curved surface. The formula for its surface area is $A = 4 \pi r^2$, where $r$ is the radius of the sphere.

A hemisphere is half of a sphere. Its curved surface area (CSA) is half the surface area of the full sphere, given by the formula $CSA = 2 \pi r^2$.

The total surface area (TSA) of a hemisphere is the sum of its curved surface area and the area of its flat circular base. The formula is $TSA = 2 \pi r^2 + \pi r^2 = 3 \pi r^2$.

The volume of a sphere is calculated using the formula $V = \frac{4}{3} \pi r^3$, where $r$ is the radius of the sphere.

The volume of a hemisphere is half the volume of a full sphere. The formula is $V = \frac{2}{3} \pi r^3$, where $r$ is the radius.

The volume of a cone is exactly one-third the volume of a cylinder that has the same base radius ($r$) and the same height ($h$). This means $3 \times \text{Volume of Cone} = \text{Volume of Cylinder}$.

Remember that surface area is a two-dimensional measure and is always expressed in square units (like $\text{cm}^2$ or $\text{m}^2$). Volume is a three-dimensional measure and is expressed in cubic units (like $\text{cm}^3$ or $\text{m}^3$).

In calculations, the value of Pi ($\pi$) is usually approximated. Use $\pi \approx \frac{22}{7}$ or $\pi \approx 3.14$ as specified in the question.