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Difficulty: MediumPerimeter and Area of 2D Figures

A circular metal plate has a total area of 100π cm2100\pi \text{ cm}^2. A smaller circular hole is drilled completely out of its exact center. If the area of the remaining metal plate is 64π cm264\pi \text{ cm}^2, what is the radius of the drilled hole?

  1. 6 cm6 \text{ cm}Answer
  2. B
    12 cm12 \text{ cm}
  3. C
    18 cm18 \text{ cm}
  4. D
    36 cm36 \text{ cm}

Answer

The radius of the drilled hole is 6 cm6 \text{ cm}.
The area of the removed hole is the difference between the original total area and the remaining area, which is 100π−64π=36π cm2100\pi - 64\pi = 36\pi \text{ cm}^2. Using the circle area formula (A=πr2A = \pi r^2), setting πr2=36π\pi r^2 = 36\pi yields r2=36r^2 = 36. Taking the square root of both sides confirms the radius is 6 cm6 \text{ cm}.

Step-by-Step Solution

1
Find the area of the drilled hole by subtracting the remaining area from the total area.
100π−64π=36π cm2100\pi - 64\pi = 36\pi \text{ cm}^2.
The drilled hole accounts for the area that was removed from the total plate.
2
Set up the area formula for the drilled hole to solve for the unknown radius.
A=πr2→36π=πr2A = \pi r^2 \rightarrow 36\pi = \pi r^2.
The area of a circle is calculated using the formula A=πr2A = \pi r^2.
3
Solve the equation for the radius rr.
r2=36r^2 = 36, so r=6 cmr = 6 \text{ cm}.
Dividing both sides by π\pi leaves r2=36r^2 = 36, and taking the square root of both sides gives the radius.

Key Concept

Perimeter and Area of 2D Figures
Estimated Time:1m 0s
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Topics

Perimeter and Area of 2D Figures

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