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

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 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 $\pi$.

Two identical right circular cones, each of radius $3\,$cm and height $7\,$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 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 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 $10\,\text{cm}\times6\,\text{cm}\times8\,\text{cm}$ surmounted by a half‐cylinder of radius $3\,$cm and length $10\,$cm on its $10\times6$ face. Calculate the total volume of the solid.

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

A triangular prism has a right‐angled triangular cross‐section with legs $4\,$cm and $3\,$cm, and length $10\,$cm. On one of its rectangular faces of dimensions $10\times3$, a half‐cylinder of radius $2\,$cm and length $10\,$cm is attached. Find the volume of the composite solid.

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 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 $\pi$.

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