Question

marks LXL Search topics and skills Q Q Welcome, Learning Diagnostic Analytics Recommendations Skill plans 4 Math Language arts of Science Social studies GA Stan Eighth grade > T.11 Volume of cones YYR The volume of this cone is 2,110.08 cubic centimeters. What is the radius of this cone? Use a 3.14 and round your answer to the nearest hundredth. 14 cm centimeters Submit

Answer 1

EXPLANATION

The radius of a cone is given by the following relationship:

`\text{Volume}=(1)/(3)\cdot\pi\cdot r^2\cdot h`

We have Volume=V= 2,110.08 cm^3 and the height is h=14cm

Replacing terms:

`2,110.08=(1)/(3)\cdot\pi\cdot r^2\cdot14`

Multiplying both sides by 3:

`2,110.08\cdot3=\pi\cdot r^2\cdot14`

Dividing both sides by 14*pi:

`(2,110.08\cdot3)/(14\cdot\pi)=r^2`

Applying the square root to both sides:

`\sqrt[]{(2,110.08\cdot3)/(14\cdot\pi)}=r`

Switching sides:

`r=\sqrt[]{(2,110.08\cdot3)/(14\cdot3.14)}`

Simplifying:

`r=\sqrt[]{144}`

Simplifying:

`r=12`

The answer is r=12 centimeters