Question

A large traffic cone stands 28 inches in height and has a volume of 732.7 cubic inches. What is the diameter of the base of the cone? Use 3.14 for pi. Show your work

Answer 1

Answer:

$d=10.0002\ inches$

Step-by-step explanation:

Given That:

Height=h=28 inches

Volume=V=732.7 cubic inches

Required:

Diameter of the base of the cone=d=?

Solution:

the formula for the volume of a cone is

$V=\frac{1}{3}\pi\ r^{2}h$

re-arranging the terms to get the radius (r)

$r^{2}= \frac{3V}{\pi h}\\r=\sqrt{\frac{3V}{\pi h}}$

putting values, we get

$r=\sqrt{\frac{3(732.7)}{3.14(28)} }$

$r=\sqrt{\frac{2198.1}{87.92} } \\r=\sqrt{25.001}\\ r=5.0001\ inches$

to find the diameter we know that diameter is double of the radius so$d=2r\\d=2(5.0001)\\d=10.0002 \ inches$