Question

Po The diameter of a circular fountain in a city park is 28 feet. A sidewalk that is 3.5 feet will be built around the fountain. Find the area of the sidewalk rounded to the tenths place. 0.8 bag of concrete will be needed for every square foot of the new sidewalk. What is the minimum number of bags needed?

Answer 1

Answer:

Area of sidewalk = $346.5 ft^2$

Bags of concrete = 277

Step-by-step explanation:

The diameter of the circular fountain is 28 ft. Radius = 28 / 2 = 14 ft

The thickness of the sidewalk is 3.5 ft. This means they want to add 3.5 ft to each radius of the fountain.

To find the area of the sidewalk alone, we have to find the area of the sidewalk alone and then subtract it from the area of the sidewalk and fountain.

That is:

$A_s = A_{s+f} - A_f$

The fountain is circular and its radius is 14 ft. Hence, its area will be:

$A_f = \pi r^2$

$A_f = \pi *14^2 = 616 ft^2$

The sidewalk and fountain together also form a circular shape. Their joint radius will be:

R = 14 + 3.5 = 17.5 ft

Hence, the area will be:

$A_{s + f} = \pi R^2 \\A_{s + f} = \pi * 17.5 * 17.5 = 962.5 ft^2$

Hence, the area of the sidewalk alone will be:

$A_s = 962.5 - 616 = 346.5 ft^2$

This is the area of the sidewalk.

For every square foot ($ft^2$), 0.8 bag of concrete will be used. This means that for $346.5 ft^2$:

Bags of concrete = 0.8 * 346.5 = 277.2 ≅ 277

At least 277 bags of concrete will be used for the new sidewalk.