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`

Step-by-step explanation

Step 1

find the volume of the cone:

The formula for the volume of a cone is

`\begin{gathered} V_(cone)=(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)=(1)/(3)\pi r^2h \\ V_(cone)=(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)=(4)/(3)\pi r^3`

then,let

radius= 6 inches

Now, replace.

`\begin{gathered} V_(sphere)=(4)/(3)\pi r^3 \\ V_(sphere)=(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= }(Volume_(sphere))/(lume_(cone)) \\ \text{replace} \\ Number\text{ of times=}(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