Question

The number of cubic inches in the volume of a 6-inch high cylindrical can equals the number of square inches in the area of the label that covers the lateral surface of the can. In inches, what is the radius of the can?

Answer 1

Answer:

In inches, the radius of the can is 2.

Step-by-step explanation:

Given:

The number of cubic inches in the volume of a 6-inch high cylindrical can equals the number of square inches in the area of the label that covers the lateral surface of the can.

Now, to find the radius of the can in inches.

Let the radius of can be $r.$

Height of can = $6\ inches.$

As given, the number of cubic inches of the volume of the cylindrical can equals the number of square inches in the area of the label that covers the lateral surface of the can.

So,

Volume of can = lateral surface area of can.

Now, we put formula of volume and lateral surface area of cylinder:

$\pi r^2h=2\pi rh$

$\pi \times r\times r\times 6=2\times \pi \times r\times 6$

Dividing both sides by $\pi \times r$ we get:

$r\times 6=2\times 6$

$6r=12$

Dividing both sides by 6 we get:

$r=2.$

Therefore, in inches, the radius of the can is 2.