Question

The difference between the outer and the inner curved surfaces of a cylinder 14 cm long is 88 cm². Find the outer and the inner radii of the cylinder, given that the volume of the metal is 176 cm³.

a. Outer radius = 7 cm, Inner radius = 5 cm
b. Outer radius = 8 cm, Inner radius = 6 cm
c. Outer radius = 6 cm, Inner radius = 4 cm
d. Outer radius = 5 cm, Inner radius = 3 cm

Answer 1

The outer radius of the cylinder is 2 cm, and the inner radius is 4 cm.

Step-by-step explanation:

To find the outer and inner radii of the cylinder, we need to first calculate the volume of the cylinder using the formula V = πr²h. Given that the volume of the metal is 176 cm³, we can solve for r:

176 = 3.142r²(14)
176 = 43.988r²
r² = 4
r = 2 cm

The outer radius of the cylinder is r = 2 cm. To find the inner radius, we need to subtract the thickness of the cylinder from the outer radius. Given that the difference between the outer and inner curved surfaces is 88 cm², the thickness of the cylinder is 88/14 = 6 cm. Therefore, the inner radius is r = 2 - 6 = 4 cm.