Sure! Here are some practice problems that involve estimating values of expressions with pi (π). I will provide the questions first and then give you the answers at the end.
Practice Problems
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Estimate the circumference of a circle with a radius of 5 units. Use π ≈ 3.14.
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Calculate the area of a circle with a diameter of 10 units. Use π ≈ 3.14.
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Find the volume of a cylinder with a radius of 3 units and a height of 7 units. Use π ≈ 3.14.
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Determine the length of an arc that subtends an angle of 60 degrees in a circle of radius 4 units. Use π ≈ 3.14.
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Estimate the surface area of a sphere with a radius of 6 units. Use π ≈ 3.14.
Answers
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Circumference:
\( C = 2\pi r = 2 \cdot 3.14 \cdot 5 \approx 31.4 \) units -
Area:
\( A = \pi r^2 = \pi \left(\frac{10}{2}\right)^2 = \pi \cdot 25 \approx 78.5 \) square units -
Volume:
\( V = \pi r^2 h = \pi \cdot 3^2 \cdot 7 = \pi \cdot 9 \cdot 7 \approx 197.82 \) cubic units -
Length of Arc:
\( L = \frac{\theta}{360} \cdot 2\pi r = \frac{60}{360} \cdot 2 \cdot 3.14 \cdot 4 = \frac{1}{6} \cdot 25.12 \approx 4.19 \) units -
Surface Area:
\( SA = 4\pi r^2 = 4 \cdot \pi \cdot 6^2 = 4 \cdot \pi \cdot 36 \approx 452.16 \) square units
Feel free to try solving these problems on your own before checking the answers!
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