Question

dont forget!
the area of a circle is equal to the radius squared times 3.14.
\text{area of circle} = \text{radius} \times \text{radius} \times 3.14
= \text{radius}^2 \times 3.14

1 what is the area of each circle below?
(1) a circle with radius 3 in.
(3^2 \times 3.14 =)
(ans.)

(2) a circle with radius 5 in.
(ans.)

(3) a circle with diameter 12 in.
(ans.)

(4) a circle with diameter 16 in.
(ans.)

2 what is the area of each shape below?
(1) a semicircle with radius 4 cm.
(4^2 \times 3.14 \times \frac{1}{2} =)
(ans.)

(2) a semicircle with diameter 4 cm.
(ans.)

(3) a quadrant (quarter circle) with radius 5 cm.
(ans.)

(4) a quadrant (quarter circle) with radius 6 cm.
(ans.)

Explanation:

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<reasoning>

Identify formulas for each shape

The area of a circle is calculated using:
\[A = r^2 \times 3.14\]
where \(r\) is the radius. If given the diameter \(d\), the radius is \(r = \frac{d}{2}\).
For a semicircle (half circle), the area is:
\[A = r^2 \times 3.14 \times \frac{1}{2}\]
For a quarter circle (sector with a \(90^\circ\) angle), the area is:
\[A = r^2 \times 3.14 \times \frac{1}{4}\]

Calculate areas for Question 1

• (1) Radius \(r = 3\text{ in}\).

\[A = 3^2 \times 3.14 = 9 \times 3.14 = 28.26\text{ sq in}\]

• (2) Radius \(r = 5\text{ in}\).

\[A = 5^2 \times 3.14 = 25 \times 3.14 = 78.5\text{ sq in}\]

• (3) Diameter \(d = 12\text{ in}\), so radius \(r = 6\text{ in}\).

\[A = 6^2 \times 3.14 = 36 \times 3.14 = 113.04\text{ sq in}\]

• (4) Diameter \(d = 16\text{ in}\), so radius \(r = 8\text{ in}\).

\[A = 8^2 \times 3.14 = 64 \times 3.14 = 200.96\text{ sq in}\]

Calculate areas for Question 2

• (1) Semicircle with radius \(r = 4\text{ cm}\).

\[A = 4^2 \times 3.14 \times \frac{1}{2} = 16 \times 3.14 \times 0.5 = 25.12\text{ sq cm}\]

• (2) Semicircle with radius \(r = 4\text{ cm}\).

\[A = 4^2 \times 3.14 \times \frac{1}{2} = 16 \times 3.14 \times 0.5 = 25.12\text{ sq cm}\]

• (3) Quarter circle with radius \(r = 5\text{ cm}\).

\[A = 5^2 \times 3.14 \times \frac{1}{4} = 25 \times 3.14 \times 0.25 = 19.625\text{ sq cm}\]

• (4) Quarter circle with radius \(r = 6\text{ cm}\).

\[A = 6^2 \times 3.14 \times \frac{1}{4} = 36 \times 3.14 \times 0.25 = 28.26\text{ sq cm}\]
</reasoning>

<answer>

Question 1

No.	Problem	Answer
(2)	\(5^2 \times 3.14\)	\(78.5\text{ sq in}\)
(3)	\(6^2 \times 3.14\)	\(113.04\text{ sq in}\)
(4)	\(8^2 \times 3.14\)	\(200.96\text{ sq in}\)

Question 2

No.	Problem	Answer
(2)	\(4^2 \times 3.14 \times \frac{1}{2}\)	\(25.12\text{ sq cm}\)
(3)	\(5^2 \times 3.14 \times \frac{1}{4}\)	\(19.625\text{ sq cm}\)
(4)	\(6^2 \times 3.14 \times \frac{1}{4}\)	\(28.26\text{ sq cm}\)

</answer>

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Answer:

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<reasoning>

Identify formulas for each shape

The area of a circle is calculated using:
\[A = r^2 \times 3.14\]
where \(r\) is the radius. If given the diameter \(d\), the radius is \(r = \frac{d}{2}\).
For a semicircle (half circle), the area is:
\[A = r^2 \times 3.14 \times \frac{1}{2}\]
For a quarter circle (sector with a \(90^\circ\) angle), the area is:
\[A = r^2 \times 3.14 \times \frac{1}{4}\]

Calculate areas for Question 1

• (1) Radius \(r = 3\text{ in}\).

\[A = 3^2 \times 3.14 = 9 \times 3.14 = 28.26\text{ sq in}\]

• (2) Radius \(r = 5\text{ in}\).

\[A = 5^2 \times 3.14 = 25 \times 3.14 = 78.5\text{ sq in}\]

• (3) Diameter \(d = 12\text{ in}\), so radius \(r = 6\text{ in}\).

\[A = 6^2 \times 3.14 = 36 \times 3.14 = 113.04\text{ sq in}\]

• (4) Diameter \(d = 16\text{ in}\), so radius \(r = 8\text{ in}\).

\[A = 8^2 \times 3.14 = 64 \times 3.14 = 200.96\text{ sq in}\]

Calculate areas for Question 2

• (1) Semicircle with radius \(r = 4\text{ cm}\).

\[A = 4^2 \times 3.14 \times \frac{1}{2} = 16 \times 3.14 \times 0.5 = 25.12\text{ sq cm}\]

• (2) Semicircle with radius \(r = 4\text{ cm}\).

\[A = 4^2 \times 3.14 \times \frac{1}{2} = 16 \times 3.14 \times 0.5 = 25.12\text{ sq cm}\]

• (3) Quarter circle with radius \(r = 5\text{ cm}\).

\[A = 5^2 \times 3.14 \times \frac{1}{4} = 25 \times 3.14 \times 0.25 = 19.625\text{ sq cm}\]

• (4) Quarter circle with radius \(r = 6\text{ cm}\).

\[A = 6^2 \times 3.14 \times \frac{1}{4} = 36 \times 3.14 \times 0.25 = 28.26\text{ sq cm}\]
</reasoning>

<answer>

Question 1

No.	Problem	Answer
(2)	\(5^2 \times 3.14\)	\(78.5\text{ sq in}\)
(3)	\(6^2 \times 3.14\)	\(113.04\text{ sq in}\)
(4)	\(8^2 \times 3.14\)	\(200.96\text{ sq in}\)

Question 2

No.	Problem	Answer
(2)	\(4^2 \times 3.14 \times \frac{1}{2}\)	\(25.12\text{ sq cm}\)
(3)	\(5^2 \times 3.14 \times \frac{1}{4}\)	\(19.625\text{ sq cm}\)
(4)	\(6^2 \times 3.14 \times \frac{1}{4}\)	\(28.26\text{ sq cm}\)

</answer>

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