The volume of a cylinder is 20 ft. Which expression represents the volume of a cone with the same base and height as the cylinder? 2.43 30 R 20 ft 3 3(20) ft 1 2004

Question

asked Feb 20, 2021 169k views

2 Answers

Nextzeus · Answer 1 · 2021-02-25T10:57:03+0000

Explanation:

We have,

Volume of cylinder is 20 ft,
$V_1=20\ ft$

It is required to find the expression that represents the volume of a cone with the same base and height as the cylinder.

Let
V_2 is volume of cone. The formula of the volume of cylinder and the cone is given by :

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

Dividing the above formulas as :

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

V_2=(V_1)/(3)

$V_2=(20)/(3)\ ft$

So, the volume of a cone is
$(20)/(3)\ ft$ .