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

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

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 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.

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 right circular cones of radius $5\text{ cm}$ and height $12\text{ cm}$ are attached base to base. Compute 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 face of the central cube. Find the total surface area of the arrangement.

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 rectangular prism measures $12\times8\times5\text{ cm}$. A square-based pyramid of base $8\times8\text{ cm}$ and height $6\text{ cm}$ is attached to the $12\times8$ face. Calculate the total surface area of the composite solid.

A cylinder of radius $5\text{ cm}$ and height $15\text{ cm}$ has a square prism hole of cross section $6\text{ cm}\times6\text{ cm}$ drilled completely through its axis. Calculate the total surface area of the hollow solid.

A triangular prism has an equilateral triangle cross section of side $8\text{ cm}$ and length $12\text{ cm}$. A 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 right circular cone of radius $3\text{ cm}$ and height $4\text{ cm}$ is glued by its base to a hemisphere of the same radius, and another identical cone is glued to the flat face of the hemisphere. Calculate the total surface area of the resulting solid.