Question

How many times greater is the volume of the Sphere than the volume of Cone #1? Round your answer to the nearest tenth.

Answer 1

$Number\text{ of times=}4.8$

Explanation

Step 1

find the volume of the cone:

The formula for the volume of a cone is

$\begin{gathered} V_{cone}=\frac{1}{3}\pi r^2h \\ \end{gathered}$

where

then , to find the volume of cone"1

let

r= 6 in

h=5 in

Now, replace

$\begin{gathered} V_{cone}=\frac{1}{3}\pi r^2h \\ V_{cone}=\frac{1}{3}\pi(6In)^2)(5in) \\ V_{cone}=60\pi in^3 \\ V_{cone}=188.495in^3 \\ \end{gathered}$

Step 2

Now, the volume of a sphere:

The formula for the volume of a sphere is

$V_{sphere}=\frac{4}{3}\pi r^3$

then,let

radius= 6 inches

Now, replace.

$\begin{gathered} V_{sphere}=\frac{4}{3}\pi r^3 \\ V_{sphere}=\frac{4}{3}\pi(6in)^3 \\ V_{sphere}=288\text{ }\pi in^3 \\ V_{sphere}=904.778in^3 \end{gathered}$

Step 3

finally, to know how many times the volume of the sphere is greater than the volume of the cone , do a division

$\begin{gathered} Number\text{ of times= }\frac{Volume_{sphere}}{lume_{cone}} \\ \text{replace} \\ Number\text{ of times=}\frac{904.778in^3}{188.495in^3} \\ Number\text{ of times=}4.80 \\ \text{rounded to the nearesth tenth} \\ Number\text{ of times=}4.8 \end{gathered}$

so, the answer is 4.8

I hope this helps you