Find the area of a circle

The Formula for the Area of a Circle

1 pts

volume_mute

When a circle is cut into many equal pie-shaped pieces and rearranged, the result resembles a parallelogram whose base is half the circumference and whose height equals the radius.

The area of a circle with radius $r$ is given by the formula:

\[A = \pi r^2\]

In the expression $\pi r^2$, what operations are indicated?

Add π and then square r

Multiply π by r, then square the result

Square r first, then multiply by π

Multiply π by 2, then multiply by r

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Find the Radius from the Diameter

1 pts

volume_mute

Before computing the area of the circle below, the radius must be found. The diameter is labeled on the figure.

Since the length of the diameter is 10 cm and the diameter is twice the length of the radius, what is the radius?

2 cm

5 cm

10 cm

20 cm

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Area of a Circle – Exact Answer (d = 10 cm)

2 pts

volume_mute

Find the exact area of the circle shown below. Leave the answer in terms of $\pi$.

$5\pi$ cm²

$10\pi$ cm²

$25\pi$ cm²

$100\pi$ cm²

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Area of a Circle – Approximation (d = 10 cm)

1 pts

volume_mute

The exact area of the circle with diameter 10 cm is $25\pi$ cm². Using a calculator, approximate the area to the nearest tenth.

75.2 cm²

76.8 cm²

78.5 cm²

80.1 cm²

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Area of a Circle – Exact Answer (d = 12 ft)

2 pts

volume_mute

Find the exact area of a circle with a diameter of 12 feet. Leave the answer in terms of $\pi$.

$12\pi$ ft²

$24\pi$ ft²

$36\pi$ ft²

$144\pi$ ft²

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Area of a Circle – Approximation (d = 12 ft)

1 pts

volume_mute

The exact area of the circle with diameter 12 ft is $36\pi$ ft². Approximate the area to the nearest tenth.

110.4 ft²

111.2 ft²

112.5 ft²

113.1 ft²

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Helicopter Landing Pad – Area and Cost of Paint

3 pts

volume_mute

Orange paint is available in gallon containers at $19 each, and each gallon covers 375 ft². A circular helicopter landing pad has a diameter of 60 feet. How much will it cost to paint the pad?

How many gallons of paint must be purchased, and what is the total cost?

7 gallons → $133

8 gallons → $152

9 gallons → $171

10 gallons → $190

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Area of a Composite Figure – Triangle and Two Semicircles

3 pts

volume_mute

Find the area of the shaded figure below. Round to the nearest hundredth.

84.20 in²

86.40 in²

88.40 in²

90.60 in²

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Area of a Composite Figure – Larger Triangle and Two Semicircles

3 pts

volume_mute

Find the area of the shaded figure below. Round to the nearest hundredth.

404.73 yd²

414.73 yd²

424.73 yd²

434.73 yd²

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Explanation

Complete the Area Formulas

3 pts

Drag the correct expression into each placeholder.

Full circle area: $A = \pi$ × (1)

Semicircle area: $A = $ (2) $\times \pi r^2$

In the 6–8–10 composite figure:
Triangle area = ½ × 6 × 8 = (3) in²
Smaller semicircle ($r=4$) area = (4) $\pi$ in²
Larger semicircle ($r=5$) area = (5) $\pi$ in²

Please drag and drop the selected option in the right place or type it instead

r²

½

24

8

12.5

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The Formula for the Area of a Circle

Correct Answer

Explanation

Find the Radius from the Diameter

Correct Answer

Explanation

Area of a Circle – Exact Answer (d = 10 cm)

Correct Answer

Explanation

Area of a Circle – Approximation (d = 10 cm)

Correct Answer

Explanation

Area of a Circle – Exact Answer (d = 12 ft)

Correct Answer

Explanation

Area of a Circle – Approximation (d = 12 ft)

Correct Answer

Explanation

Helicopter Landing Pad – Area and Cost of Paint

Correct Answer

Explanation

Area of a Composite Figure – Triangle and Two Semicircles

Correct Answer

Explanation

Area of a Composite Figure – Larger Triangle and Two Semicircles

Correct Answer

Explanation

Complete the Area Formulas

Correct Answer

Explanation

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