Question Type 4: Calculating the volume of specific 3D shapes given the parameters Exercises

A solid capsule consists of a cylinder of length $20 \text{ cm}$ and radius $3 \text{ cm}$ with a hemisphere attached to each end.

Find the total volume in $\text{cm}^3$ in terms of $\pi$.

Find the volume of a right triangular prism whose cross‐section is a right triangle with legs $6\text{ cm}$ and $8\text{ cm}$ and whose prism length is $15\text{ cm}$.

A frustum of a right circular cone has top radius $4\text{ cm}$, base radius $7\text{ cm}$, and height $12\text{ cm}$. Compute its volume in $\text{cm}^3$.

A hemisphere has diameter $14\text{ cm}$. Calculate its volume.

A rectangular block measures $10\text{ cm}\times8\text{ cm}\times6\text{ cm}$. A cylindrical hole of radius $2\text{ cm}$ is drilled through the centre along the $6\text{ cm}$ dimension. Find the volume of the remaining solid, to the nearest $\text{cm}^3$.

Find the volume of a right circular cylinder with radius $4\text{ cm}$ and height $10\text{ cm}$.

Determine the volume of a sphere of radius $6\text{ cm}$.

A right circular cone has base diameter $12 \text{ cm}$ and slant height $10 \text{ cm}$. Calculate its volume, correct to 1 decimal place.

Calculate the volume of a square pyramid with base edge $9 \text{ cm}$ and height $12 \text{ cm}$.

Find the volume of a right circular cylinder with radius $4\text{ cm}$ and height $9\text{ cm}$. Give your answer in terms of $\pi$ and as a decimal to 3 s.f.

Calculate the volume of a rectangular prism with length $8\text{ cm}$, width $5\text{ cm}$, and height $3\text{ cm}$.

A solid consists of a right circular cylinder of radius $3\text{ cm}$ and height $10\text{ cm}$ topped by a hemisphere of the same radius. Find its total volume.

Compute the volume of a right circular cone with base radius $3\text{ cm}$ and height $7\text{ cm}$.