It looks like you've uploaded a page from a math worksheet or textbook focused on
finding the volumes of spheres, pyramids, and cones. The content includes:
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Pre-knowledge review: Concepts such as calculating areas and using formulas.
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Formulas for volume:
- Sphere: $ V = \frac{4}{3} \pi r^3 $
- Pyramid: $ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} $
- Cone: $ V = \frac{1}{3} \pi r^2 h $
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Examples and practice problems with diagrams.
Since I can't view images directly, I'll explain how to solve typical problems from this type of worksheet based on the visible text and common structure.
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🔷 Example Problem: Volume of a Sphere
Problem: Find the volume of a sphere with radius 5 cm.
Solution:
Use the formula:
$$
V = \frac{4}{3} \pi r^3
$$
Substitute $ r = 5 $:
$$
V = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) = \frac{500}{3} \pi \approx 523.6 \text{ cm}^3
$$
✔ Answer: $ \frac{500}{3} \pi $ cm³ or approximately
523.6 cm³
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🔷 Example Problem: Volume of a Pyramid
Problem: A pyramid has a square base with side length 6 cm and height 9 cm. Find its volume.
Solution:
Base area = $ 6 \times 6 = 36 $ cm²
Height = 9 cm
Use the formula:
$$
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
= \frac{1}{3} \times 36 \times 9 = 108 \text{ cm}^3
$$
✔ Answer: 108 cm³
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🔷 Example Problem: Volume of a Cone
Problem: A cone has a radius of 4 cm and height of 10 cm. Find its volume.
Solution:
$$
V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (4)^2 (10) = \frac{1}{3} \pi (16)(10) = \frac{160}{3} \pi \approx 167.6 \text{ cm}^3
$$
✔ Answer: $ \frac{160}{3} \pi $ cm³ or approximately
167.6 cm³
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📌 Key Tips:
- Always ensure units are consistent.
- Use $ \pi \approx 3.14 $ or leave in terms of $ \pi $ unless specified.
- For pyramids and cones, remember the $ \frac{1}{3} $ factor — it’s easy to forget!
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If you can describe a specific problem from the image (e.g., "Find the volume of a cone with radius 3 and height 7"), I can walk you through that exact solution step-by-step.
Let me know!
Parent Tip: Review the logic above to help your child master the concept of volume of spheres cones and cylinders worksheet.
