IB Mathematics Analysis and Approaches 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.