Question

A circular fountain with a radius of 7 m is encircled by a grass bed that is 3.5 m wide. Determine the ratio of the area of the grass bed to the area of the fountain.

• A. 3:2
• B. 2:1
• C. 5:4
• D. 4:1

Answer 1

Answer:

C. 5:4

Given:

• Radius of fountain = 7 m

• Width of grass bed = 3.5 m

• Outer radius = (7+3.5=10.5) m

Step 1: Area of the grass bed

$=\pi(10.5)^2-\pi(7)^2$
$=\pi(110.25-49)=61.25\pi$

Step 2: Area of the fountain

$=49\pi$

Step 3: Ratio

$61.25\pi:49\pi$

$=61.25:49$

Multiplying by 4:

$245:196=\boxed{5:4}$

Answer: 5 : 4