Question

A company makes steel rods shaped like cylinders. Each rod has a radius of 3 centimeters and a height of 20 centimeters. If the company used 45,781.2 of steel, how many rods did it make?

Answer 1

80 rods of steel.

Explanation:

Here is the complete question

A company makes steel rods shaped like cylinders. Each rod has a radius of 3 centimeters and a height of 20 centimeters. If the company used 45,781.2 cm³ of steel, how many rods did it make?

Solution

Since the steel rod is a cylinder whose volume, V = πr²h where r = radius of cylinder = 3 cm and h = height of cylinder = 20 cm.

We substitute these into V to find the volume of one rod.

So, V = πr²h

= π(3 cm)² × 20 cm

= π × 9 cm² × 20 cm

= 180π cm³

= 565.49 cm³

Since 45,781.2 cm³ of steel was used, this total volume of steel, V' equals the number of rods, n times the volume of one rod, V.

So, V' = nV

Making n subject of the formula, we have

n = V'/V

Substituting V' and V into the equation, we have

n = 45,781.2 cm³/565.49 cm³

n = 80.96

We round n = 80.96 down to 80 since we cannot have a decimal number of rods.

So, n = 80 rods

So, the company made are 80 rods of steel.