Question

A cone-shaped paper cup can hold 35 cubic inches of food. If the radius of the cone is 2.4 inches, what is the height of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth.
5.81 inches
6.57 inches
7.89 inches
8.89 inches

Answer 1

35 = $\frac{1}{3}$ (3.14)(r²)(2.4)
35 = $\frac{1}{3}$ (7.536)(r²)
35 = 2.512 r²

35 ÷ 2.512 = 14
2.512 ÷ 2.512 = 1
14 ≈ r²
√14 ≈ √r²
3.74165 ≈ r

I'd say A would be the answer!

Answer 2

Answer: 5.81 inches

Step-by-step explanation:

The formula of volume of cone is given by :-

$\text{V}=\dfrac{1}{3}\pi r^2 h$, where r is the radius and h is height  of the cone.

Given: Volume of cone =  35 cubic inches

The radius of cone = 2.4 inches

$\Rightarrow 35=\dfrac{1}{3}\pi (2.4)^2 h\\\\\Rightarrow\ h=\dfrac{35\times3}{(2.4)^2(3.14)}\\\\\Rightarrow\ h=5.8054670913\approx5.81 \text{ inches}$

Hence, the height of the cone is 5.82 inches.