Round your answer to two decimal places.
-The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 8 inches?
A) $50.24 \mathrm { in } ^ { 2 }$
B) $25.12 \mathrm { in } ^ { 2 }$
C) $200.96$ in $^ { 2 }$
D) $203.36$ in $^ { 2 }$

Question

Round your answer to two decimal places.
-The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 8 inches? 
A) $50.24 \mathrm { in } ^ { 2 }$
B) $25.12 \mathrm { in } ^ { 2 }$
C) $200.96$ in $^ { 2 }$
D) $203.36$ in $^ { 2 }$

Quizplus · Accepted Answer

The area of a circle is given by the formula $A = \pi r^2$, where $A$ is the area and $r$ is the radius. The problem states that the area varies directly with the square of the radius, which is consistent with this formula. Given the area for a radius of 5 inches, we can find the area for a radius of 8 inches by using the direct variation relationship. The calculation is as follows: $\frac{78.5}{5^2} = \frac{A}{8^2}$, solving for $A$ gives $A = 200.96$ square inches.

Round Your Answer to Two Decimal Places 50.24in250.24 \mathrm { in } ^ { 2 }50.24in2

Round Your Answer to Two Decimal Places $50.24 \mathrm { in } ^ { 2 }$