Question

The Blackwells have a circular pool with a radius of 10 feet. They plan on installing a 3 -foot-wide walkway around the pool. What will be the area of the walkway? A $216.8 \mathrm{ft}^{2}$ C $314.2 \mathrm{ft}^{2}$ B $285.9 \mathrm{ft}^{2}$ D $442.2 \mathrm{ft}^{2}$ (IMAGES CANNOT COPY)

Name: Problem 40, Chapter 10: Prealgebra
Uploaded: 2020-05-20T01:14:05-08:00
Duration: 2 min 6 s
Channel: Christopher Stanley
Description: The Blackwells have a circular pool with a radius of 10 feet. They plan on installing a 3 -foot-wide walkway around the pool. What will be the area of the walkway? A 216.8 ft^2 C 314.2 ft^2 B 285.9 ft^2 D 442.2 ft^2 (IMAGES CANNOT COPY)

   The Blackwells have a circular pool with a radius of 10 feet. They plan on installing a 3 -foot-wide walkway around the pool. What will be the area of the walkway?
A $216.8 \mathrm{ft}^{2}$
C $314.2 \mathrm{ft}^{2}$
B $285.9 \mathrm{ft}^{2}$
D $442.2 \mathrm{ft}^{2}$
(IMAGES CANNOT COPY)

Prealgebra

Carol E. Malloy,… 1st Edition

Chapter 10, Problem 40

Instant Answer

Solved by Expert Christopher Stanley

05/20/2020

Step 1

The radius of this circle is the sum of the radius of the pool and the width of the walkway, which is $10 + 3 = 13$ feet. The formula for the area of a circle is $\pi r^{2}$, so the area of the larger circle is $\pi (13)^{2} = 530.9$ square feet. Show more…

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The Blackwells have a circular pool with a radius of 10 feet. They plan on installing a 3 -foot-wide walkway around the pool. What will be the area of the walkway? A $216.8 \mathrm{ft}^{2}$ C $314.2 \mathrm{ft}^{2}$ B $285.9 \mathrm{ft}^{2}$ D $442.2 \mathrm{ft}^{2}$ (IMAGES CANNOT COPY)

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Key Concepts

Area of an Annulus

An annulus is the region between two concentric circles. Its area is found by subtracting the area of the smaller circle from the area of the larger circle, using the formula A = ?(R² - r²), where R is the outer radius and r is the inner radius. This concept is crucial for problems involving paths or borders around circular areas.

Area of a Circle

This concept involves calculating the area of a circle using the formula A = ?r², where r represents the radius. It is fundamental in geometry for determining the space occupied by a circular object.

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