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About how much does the area of a circle increases when the radius increases from 3cm to 5cm?

A. 2cm^2
B. 13cm^2
C. 25cm^2
D. 50cm^2

User Jagmag
by
4.1k points

2 Answers

0 votes

Answer:

The answer would be C

Explanation:

The area of a circle:

A = πr²

dA/dr = 2πr

We are given dA/dt, using the chain rule

dr/dt = dA/dt x dr/dA

dr/dt = 1 x 1/2πr

When circumference = 2 cm:

2 = 2πr

r = 1/π; putting this value of r

dr/dt = 1/2π(1/π)

dr/dt = 1/2 cm/s

The radius is increasing at a rate of 1/2 cm/s.

User Shahar
by
4.2k points
2 votes
C is probably the best choice
User Mediocre Gopher
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4.4k points