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

A right circular cylinder of radius $7\text{ cm}$ and height $12\text{ cm}$ has a right circular cone of the same base radius attached to one of its circular faces. The cone has slant height $15\text{ cm}$. Calculate the total surface area of the combined solid. Give your answer in terms of $\pi$.

A rectangular prism measures $12 \times 8 \times 5 \text{ cm}$. A square-based pyramid of base $8 \times 8 \text{ cm}$ and height $6 \text{ cm}$ is attached to the $12 \times 8$ face. Calculate the total surface area of the composite solid.

A solid consists of a right circular cylinder of radius $5\text{ cm}$ and height $10\text{ cm}$ with hemispheres of radius $5\text{ cm}$ attached to both its bases. Find the total surface area.

Two identical cubes of edge length $5\text{ cm}$ are joined along one face. Calculate the total surface area of the resulting solid. [2 marks]

Two identical right circular cones of radius $5\text{ cm}$ and height $12\text{ cm}$ are attached base to base. Calculate the total surface area of the resulting solid.

Five identical cubes of side $2 \text{ cm}$ are arranged with one central cube and one attached to each of four faces of the central cube. Find the total surface area of the arrangement.

Two cubes of edge lengths $4\text{ cm}$ and $6\text{ cm}$ are joined by aligning one face of the smaller cube to a face of the larger cube. Determine the total surface area of the resulting solid.

A triangular prism has an equilateral triangle cross section of side $8\text{ cm}$ and length $12\text{ cm}$. A half-cylinder of radius $4\text{ cm}$ and height $12\text{ cm}$ is attached along one rectangular face of the prism. Determine the total surface area of the composite solid.

A cube of edge length $10\text{ cm}$ has a square-based pyramid attached to its top face. The pyramid has base side $10\text{ cm}$ and height $6\text{ cm}$. Find the total surface area of the composite solid.

A solid is formed by attaching a hemisphere of radius $3\text{ cm}$ to one end of a right circular cylinder of radius $3\text{ cm}$ and height $8\text{ cm}$. Find the total surface area of the composite solid.

A right circular cone of radius $3\text{ cm}$ and height $4\text{ cm}$ is joined by its base to one end of a cylinder of the same radius and height $3\text{ cm}$. Another identical cone is joined by its base to the other end of the cylinder. Calculate the total surface area of the resulting solid, giving your answer in terms of $\pi$.

A cylinder of radius $5 \text{ cm}$ and height $15 \text{ cm}$ has a square prism hole of cross section $6 \text{ cm} \times 6 \text{ cm}$ drilled completely through its axis. Calculate the total surface area of the hollow solid.