Question

1. find the height of a cone with a radius of 4 ft and a volume of 1005 ft³. round to the nearest foot. we know

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.

Step2: Rearrange formula for height

We can rewrite the formula to solve for $h$: $h = \frac{3V}{\pi r^{2}}$.

Step3: Substitute given values

Given $V = 1005$ ft³ and $r = 4$ ft. Substitute into the formula: $h=\frac{3\times1005}{\pi\times4^{2}}$.

Step4: Calculate the value

First, calculate the denominator $\pi\times4^{2}=\pi\times16\approx3.14\times16 = 50.24$. Then, $3\times1005 = 3015$. So $h=\frac{3015}{50.24}\approx60$ ft.

Answer:

60 ft