Question

a right cone has a volume of 314.16 cm³ and a radius of 5 cm. what is the height, to the nearest tenth of a centimetre? a) 10.1 cm b) 11.3 cm c) 11.8 cm d) 12.0 cm

Explanation:

Step1: Recall volume formula for cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height. We need to solve for $h$.

Step2: Rearrange the formula for $h$

Starting from $V = \frac{1}{3}\pi r^{2}h$, we can get $h=\frac{3V}{\pi r^{2}}$.

Step3: Substitute given values

Given $V = 314.16\ cm^{3}$ and $r = 5\ cm$. Substitute into the formula: $h=\frac{3\times314.16}{\pi\times5^{2}}$.
First, calculate the denominator: $\pi\times5^{2}=\pi\times25\approx3.14\times25 = 78.5$.
Then, calculate the numerator: $3\times314.16 = 942.48$.
So, $h=\frac{942.48}{78.5}=12$.

Answer:

d) $12.0\ cm$