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 $42$ and the height of the cylinder is $6$ . If the volume of the solid is $60 pi$ , what is the area of the base of the cylinder?

Question

1210 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-08T06:09:04

Area of base of cylinder is $3pi$

As the two have same radius, let it be $r$ .

As height of cylinder is $6$ , its volume is $6pir^2$

and as height of cone is $42$ , its volume is $1/3xxpir^2xx42=14pir^2$

and volume of solid is $6pir^2+14pir^2=20pir^2$

But as volume is $60pi$ , we have $20pir^2=60pi$

and hence $r^2=(60pi)/(20pi)=3$

and area of base of cylinder is $pir^2=pixx3=3pi$

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 60 pi60 pi, what is the area of the base of the cylinder?