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qwelly [4]
3 years ago
12

If the radius of a circle is increased by a factor of 5, the area increases by a factor of:

Mathematics
1 answer:
Darya [45]3 years ago
7 0

The area will be increased by 25. Option C

Step-by-step explanation:

Given,

The radius of a circle is increased by 5.

To find how much the area will be increased.

Let us take,

The original radius of the circle is = r

The original area = πr²

Again,

After increasing the radius = 5r

Then the area will be = π(5r)² = 25πr²

= 25( original area)

Hence,

The area will be increased by 25.

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A farmer has a 100 ft by 200 ft rectangular field that he wants to increase by 15.5% by cultivating a strip of uniform width aro
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Answer:

(a) The strip should be 5ft wide

(b) The strip around the outside field is 10ft wide.

Step-by-step explanation:

Given:

Length of the rectangular field, L= 200 ft

width of the rectangular field, w = 100 ft

Area of the rectangular field, A = 200ft x 100ft = 20000 ft^2

let the width of the strip = x

The strip around the outside field = 2x

If the field is increased by 15.5%

New area of the field = 1.155 x 20000 = 23,100 ft^2

The increase in area of the field = 3,100 ft

3,100 = New area of field - old area of the field

3100 = (200 + 2x)(100 + 2x) - 20000

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775 = 150x + x^2

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(x + 155)(x-5) = 0

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The strip should be 5ft wide.

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