Question

A farmer has three silos. The largest silo has a diameter of 24 feet. The radius of the smallest silo is one-thrid as big as the diameter of the largest. The middle sized silo has a radius that is 2 feet greater than the radius of the smallest silo. What is the circumference of each silo?

Answer 1

Answer:

Exact:

$16 \pi~ft;~~20 \pi~ft;~~24 \pi~ft$

Approximate:

50.3 ft, 62.8 ft, 75.4 ft

Step-by-step explanation:

Let's find the radius of each silo using the given information.

"The largest silo has a diameter of 24 feet."

$d_{largest} = 24~ft$

$r_{largest} = \dfrac{d_{largest}}{2} = \dfrac{24~ft}{2} = 12~ft$

"The radius of the smallest silo is one-third as big as the diameter of the largest."

$r_{smallest} = \dfrac{24~ft}{3} = 8~ft$

"The middle-sized silo has a radius that is 2 feet greater than the radius of the smallest silo."

$r_{middle} = r_{smallest} + 2~ft = 8~ft + 2~ft = 10~ft$

The three radii are: 8 ft, 10 ft, and 12 ft.

Now we use the circumference formula with each radius to find the circumferences.

Smallest:

$C = 2 \pi r = 2 \times \pi \times 8~ft = 16 \pi~ft$

Middle:

$C = 2 \pi r = 2 \times \pi \times 10~ft = 20 \pi~ft$

Largest:

$C = 2 \pi r = 2 \times \pi \times 12~ft = 24 \pi~ft$

The circumferences above are exact. If you want approximations, then use a calculator and an approximation for pi.

The circumferences are approximately: 50.3 ft, 62.8 ft, 75.4 ft