Question

A cone shaped paper cut the surface water the height of the cup is 10 cm in diameter is 8 cm. What is the radius of the cone? What is the volume of the paper cup?

Answer 1

Given:

height of the cup = 10 cm

diameter = 8 cm

Let us begin by illustrating the problem on a diagram:

The base of the cone is a circle. Hence, its diameter(d) and radius(r) are related by the formula:

$r\text{ = }\frac{d}{2}$

Hence, the radius of the cone is:

$\begin{gathered} r\text{ = }\frac{8}{2} \\ =\text{ 4 cm} \end{gathered}$

The volume (V) of the paper cup can be found using the formula:

$\begin{gathered} V\text{ = }\frac{1}{3}\pi r^2h \\ Where\text{ r is the radius} \\ h\text{ is the height} \end{gathered}$

Hence, the volume (V) of the paper cup:

$\begin{gathered} V\text{ = }\frac{1}{3}\times\pi\times\text{ 4}^2\text{ }\times\text{ 10} \\ =\text{ 167.55} \\ \approx\text{ 168 cubic cm} \end{gathered}$

Answer Summary

radius = 4 cm

volume = 168 cubic cm