Question

Pietro is planning a patio using paving stones that are circles, semicircles, and quarter-circles. All stones have a radius of 10 inches. What is the area of one pattern of stones that has 5 circles, 10 semicircles, and 100 quarter-circles? Then, select the total area.

Answer 1

3500
`\pi` = 10995.57 in³ (nearest hundredth)

Explanation:

area of a circle =
`\pi r^2`

⇒ area of a semicircle =
`(1)/(2)\pi r^2`

⇒ area of a quarter circle =
`(1)/(4)\pi r^2`

total area = 5 circles + 10 semicircles + 100 quarter circles

⇒ total area =
`5\pi r^2 +(10* (1)/(2)\pi r^2)+(100 * (1)/(4)\pi r^2)`

⇒ total area =
`35\pi r^2`

If r = 10 inches

⇒ total area =
`35\pi * 10^2=3500\pi =10995.57 \ \textsf{in}^2 \ \textsf{(nearest tenth)}`