To find the volume of a sphere, we use the formula:
$$V = \frac{4}{3} \pi r^3$$
The problem asks us to use
3.14 for $\pi$ and round the answer to the nearest hundredth. We need to find the radius ($r$) for each sphere first. The radius is half of the diameter.
Here are the step-by-step calculations for each sphere:
1. Top Left Sphere
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Given: Diameter = 2 m
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Find Radius ($r$): $2 \div 2 = 1$ m
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Calculate Volume:
$$V = \frac{4}{3} \times 3.14 \times (1)^3$$
$$V = 1.333... \times 3.14 \times 1$$
$$V \approx 4.186...$$
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Round to nearest hundredth: 4.19 m³
2. Top Right Sphere
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Given: Diameter = 8 ft
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Find Radius ($r$): $8 \div 2 = 4$ ft
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Calculate Volume:
$$V = \frac{4}{3} \times 3.14 \times (4)^3$$
$$V = \frac{4}{3} \times 3.14 \times 64$$
$$V = 1.333... \times 200.96$$
$$V \approx 267.946...$$
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Round to nearest hundredth: 267.95 ft³
3. Bottom Left Sphere
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Given: Diameter = 10 in
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Find Radius ($r$): $10 \div 2 = 5$ in
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Calculate Volume:
$$V = \frac{4}{3} \times 3.14 \times (5)^3$$
$$V = \frac{4}{3} \times 3.14 \times 125$$
$$V = 1.333... \times 392.5$$
$$V \approx 523.333...$$
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Round to nearest hundredth: 523.33 in³
4. Bottom Right Sphere
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Given: Diameter = 7 cm
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Find Radius ($r$): $7 \div 2 = 3.5$ cm
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Calculate Volume:
$$V = \frac{4}{3} \times 3.14 \times (3.5)^3$$
$$V = \frac{4}{3} \times 3.14 \times 42.875$$
$$V = 1.333... \times 134.6275$$
$$V \approx 179.503...$$
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Round to nearest hundredth: 179.50 cm³
Final Answer:
Top Left: V = 4.19 m³
Top Right: V = 267.95 ft³
Bottom Left: V = 523.33 in³
Bottom Right: V = 179.50 cm³
Parent Tip: Review the logic above to help your child master the concept of sphere worksheet.
