A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 42 42 and the height of the cylinder is 6 6. If the volume of the solid is 45 pi45π, what is the area of the base of the cylinder?

1 Answer
Mar 19, 2018

2.25pi2.25π units squared

Explanation:

To find the area, we first need to find the radius. We know that the total volume of the cylinder plus the cone is 45pi45π, which is found by adding the volumes of the cylinder (6r^2pi6r2π) and the cone ((42r^2pi)/342r2π3), where rr represents the unknown radius of the cone's and cylinder's bases.

Cylinder's volume: pir^2*hπr2h

Cone's volume: (pir^2*h)/3πr2h3

Add the two volumes together:

6r^2pi+(42r^2pi)/3=45pi6r2π+42r2π3=45π

(18r^2pi)/3 +(42r^2pi)/3=45pi18r2π3+42r2π3=45π

(60r^2pi)/3=45pi60r2π3=45π

60r^2pi=135pi60r2π=135π

60r^2=13560r2=135

r^2=2.25r2=2.25

r=+-1.5 rarrr=±1.5 Disregard the -1.5, a length cannot be negative

Area is pir^2πr2

pi*1.5^2π1.52

pi*2.25π2.25

The answer is 2.25pi2.25π