Question Type 6: Calculating the volume of specific complex shapes made by combining two or more shapes Exercises

A hemisphere of radius $7\,$cm is attached to the base of a right circular cone of the same radius and height $14\,$cm. Find the volume of the composite solid in terms of $\pi$.

A solid consists of a right circular cone of radius $4\,$cm and height $9\,$cm mounted on top of a cylinder of the same radius and height $12\,$cm. Find its total volume in $\text{cm}^3$. Give your answer in terms of $\pi$.

A cube of side length $8\,$cm has a cylindrical hole of radius $3\,$cm drilled through its center, perpendicular to one pair of faces. Calculate the volume of the remaining solid. Give your answer in terms of $\pi$.

Two identical right circular cones, each of radius $3 \text{ cm}$ and height $7 \text{ cm}$, are joined at their bases. Find the volume of the resulting solid in $\text{cm}^3$. Give your answer in terms of $\pi$.

A sphere of radius $6 \text{ cm}$ has a cylindrical hole of radius $4 \text{ cm}$ drilled straight through its centre. Find the volume of the remaining solid. Express your answer in terms of $\pi$.

A triangular prism has a right-angled triangular cross-section with legs $4 \text{ cm}$ and $3 \text{ cm}$, and length $10 \text{ cm}$. On one of its rectangular faces of dimensions $10 \times 4$, a half-cylinder of radius $2 \text{ cm}$ and length $10 \text{ cm}$ is attached. Find the volume of the composite solid.

Two hemispheres of radius $5\,$cm are joined by a right circular cylinder of radius $5\,$cm and height $10\,$cm. Calculate the volume of the entire solid in $\text{cm}^3$, in terms of $\pi$.

Calculate the volume of a solid composed of a right circular cylinder of radius $5\,$cm and height $10\,$cm, with a hemisphere of the same radius attached to one of its circular faces. Give your answer in terms of $\pi$.

A solid cylinder of radius $5 \, \text{cm}$ and height $15 \, \text{cm}$ has a right circular conical cavity of radius $3 \, \text{cm}$ and height $15 \, \text{cm}$ drilled out from one end. Calculate the remaining volume. Give your answer in terms of $\pi$.

A solid cylinder of radius $6\,$cm and height $20\,$cm has a cylindrical hole of radius $2\,$cm drilled straight through its axis for the full height. Calculate the remaining volume in terms of $\pi$.

A composite solid consists of a rectangular prism of dimensions $10 \text{ cm} \times 6 \text{ cm} \times 8 \text{ cm}$ surmounted by a half-cylinder of radius $3 \text{ cm}$ and length $10 \text{ cm}$ on its $10 \text{ cm} \times 6 \text{ cm}$ face. Calculate the total volume of the solid.