Question

7. A company makes cylindrical cans for peaches. Each can has a radius of 4 centimeters and a height of 12 centimeters. The company plans to increase the volume each day by 25%.

A) What will the height of the new can be if the radius remains the same?

B) What will be the radius of the new can if the height remains the same?

Answer 1

A ) the new can will have a height of 15 centimeters.

The volume of the original can is V = πr²h = π(4cm)²(12cm) ≈ 602.88 cm³.

To increase the volume by 25%, we need to multiply the original volume by 1.25:

V_new = 1.25V = 1.25πr²h

Since the radius remains the same, we can simplify the equation to:

V_new = πr²h_new = 1.25πr²h

Dividing both sides by πr²

So the new height of the can will be 1.25 times the original height:

Therefore, the new can will have a height of 15 centimeters.

B) the new can will have a radius of approximately 5.03 centimeters if the height remains the same.

The volume of the original can is V = πr²h = π(4cm)²(12cm) ≈ 602.88 cm³.

To increase the volume by 25%, we need to multiply the original volume by 1.25:

V_new = 1.25V = 1.25πr²h

Since the height remains the same, we can simplify the equation to:

V_new = πr_new²h = 1.25πr²h

Dividing both sides by h, we get:

πr_new² = 1.25πr²

Simplifying the equation

Taking the square root of both sides

Substituting r = 4cm, we get:

r_new = 4cm√1.25 ≈ 5.03cm

Therefore, the new can will have a radius of approximately 5.03 centimeters if the height remains the same.