Question Type 5: Calculating the surface area of specific complex shapes made by combining two or more shapes Exercises

Calculate the slant height of a right circular cone with radius $5\text{ cm}$ and height $4\text{ cm}$.

Calculate the curved surface area of a right circular cone with radius $5\text{ cm}$ and height $4\text{ cm}$.

Calculate the curved surface area of a hemisphere of radius $5\text{ cm}$.

Calculate the volume of the composite solid formed by joining a hemisphere and a right circular cone at their bases, with radius $5\text{ cm}$ and cone height $4\text{ cm}$.

Calculate the total surface area of a solid composed of a hemisphere and a right circular cone joined at their bases, where the radius of both shapes is $5\text{ cm}$ and the height of the cone is $4\text{ cm}$.

If the outside surface of the composite solid (hemisphere + cone) is to be painted at a cost of $0.05 per cm², calculate the total cost of painting the solid. Use $\pi = 3.142$ and round your answer to the nearest cent.

Find the ratio of the total curved surface area to the volume of a solid formed by joining a hemisphere and a right circular cone at their bases, given that $r=5\text{ cm}$ and $h=4\text{ cm}$. Express your answer in simplest form.

A solid is formed by casting the composite shape (hemisphere + cone) in a metal with density $7.8\text{ g/cm}^3$. Calculate the mass of the solid. Use $\pi = 3.142$ and give your answer in grams to the nearest gram.

The composite solid (hemisphere + cone) has the same volume as a right circular cylinder of radius $5\text{ cm}$. Calculate the height of this cylinder. Express your answer in terms of $\pi$.

A second composite solid is formed by joining a hemisphere and a cone, where both the radius and the height of the cone are doubled compared to the original (so $r=10\text{ cm}$, $h=8\text{ cm}$). Determine the ratio of the total surface area of the new solid to that of the original solid. Express your answer in simplest form.

A hollow shell is created by removing a smaller hemisphere of radius $4\text{ cm}$ and a smaller right circular cone of radius $4\text{ cm}$ and height $3\text{ cm}$ from the inside of the original composite solid (hemisphere + cone) with $r=5\text{ cm}$ and $h=4\text{ cm}$. Calculate the volume of the remaining material. Give your answer in terms of $\pi$.

Determine the radius of a sphere that has the same surface area as the composite solid formed by joining a hemisphere and a right circular cone with $r=5\text{ cm}$ and $h=4\text{ cm}$. Express your answer in exact form involving $\pi$.