Solve the problem.
-The area $\mathrm { A } = \pi \mathrm { r } ^ { 2 }$ of a circular oil spill changes with the radius. To the nearest tenth of a square foot, how much does the area increase when the radius changes from $7 \mathrm { ft }$ to $7.1 \mathrm { ft }$ ?
A) $4.4 \mathrm { ft } ^ { 2 }$
B) $2.8 \mathrm { ft } ^ { 2 }$
C) $44.0 \mathrm { ft } ^ { 2 }$
D) $22.0 \mathrm { ft } ^ { 2 }$

Question

Quizplus · Accepted Answer

The increase in area can be calculated using the formula for the area of a circle, $A = \pi r^2$, for both the initial and final radii, and then finding the difference. For the initial radius of 7 ft, the area is $A_1 = \pi (7)^2 = 49\pi$. For the final radius of 7.1 ft, the area is $A_2 = \pi (7.1)^2 = 50.41\pi$. The increase in area is $50.41\pi - 49\pi = 1.41\pi$, which is approximately 4.4 square feet when rounded to the nearest tenth.

Solve the Problem A=πr2\mathrm { A } = \pi \mathrm { r } ^ { 2 }A=πr2

Solve the Problem $\mathrm { A } = \pi \mathrm { r } ^ { 2 }$