A cone and cylinder have the same height and the same base radius. If the volume of the cylinder is 81 cm^3 what is the volume of the cone in cm^3? A) 9 B) 27 C) 78 D)243

Question

asked Jun 25, 2019 171k views

1 Answer

Janis Peisenieks · Answer 1 · 2019-07-02T10:10:45+0000

Answer:

The volume of the cone is
27cm^3

Explanation:

We know that formulas

Volume of cylinder is

$V_1=\pi r^2 h$

Volume of cone is

$V_2=(1)/(3)\pi r^2 h$

we are given

A cone and cylinder have the same height and the same base radius

So, both will have same radius and height

now, we can find ratios

$(V_2)/(V_1)=((1)/(3)\pi r^2h )/(\pi r^2h)$

now, we can simplify it

(V_2)/(V_1)=(1)/(3)

we are given

the volume of the cylinder is 81 cm^3

so,
V_1=81

now, we can plug it and solve for V2

(V_2)/(81)=(1)/(3)

81* (V_2)/(81)=81*(1)/(3)

V_2=27

So, the volume of the cone is
27cm^3