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The height of a cylinder is 4 times the radius of its base. The

surface area of the cylinder is 78,500 square inches. If you use
3.14 for pi, what is the volume of the cylinder?

User Alex Varga
by
3.2k points

1 Answer

6 votes

Answer:

1,570,000 cubic units

Explanation:

Surface Area of Cylinder (SA):

The surface area of a cylinder is the sum of the lateral area and the area of the two bases.

Lateral Area (LA):

The lateral area is the area of the vertical side, which is a rectangle with the circumference of the base as the length and the height of the cylinder as the width. LA = 2πrh

Base Area (BA):

The two bases are circles. BA = 2πr²

SA = 2πrh + 2πr²

The height is 4 times the radius: h = 4r

SA = 2πr(4r) + 2πr²

SA = 8πr² + 2πr²

SA = 10πr² = 78500

10(3.14)r² = 78500

r² = 2500

r = 50 units

Volume of Cylinder (V):

The volume of a cylinder is πr²h.

V = πr²h

V = 3.14 × (50)² × 4(50)

V = 1,570,000 cubic units

User Will Bellman
by
3.5k points