Math worksheet with geometry problems on volume of cones, cylinders, spheres, and hemispheres.

Let’s solve each problem one by one, using π = 3.14 and rounding to the nearest hundredth where necessary.

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Problem 10:
*A cone has a slant height of 17 cm and the base of the cone has a diameter of 14 cm. Find the height of the cone and then the volume.*

- Diameter = 14 cm → Radius (r) = 7 cm
- Slant height (l) = 17 cm

Use the Pythagorean Theorem for cones:
h² + r² = l²

→ h² + 7² = 17²
→ h² + 49 = 289
→ h² = 240
→ h = √240 ≈ 15.49 cm (rounded to nearest hundredth)

Now, volume of a cone:
V = (1/3)πr²h

→ V = (1/3)(3.14)(7²)(15.49)
→ V = (1/3)(3.14)(49)(15.49)
→ First, 49 × 15.49 = 759.01
→ Then, 3.14 × 759.01 ≈ 2384.2914
→ Divide by 3: 2384.2914 ÷ 3 ≈ 794.76 cm³

✔ Answer: Height = 15.49 cm, Volume = 794.76 cm³

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Problem 11:
*Sarah bought an extra-large soda... cup has diameter 5 inches, height 10 inches, filled 3/4 full. How many cubic inches of soda?*

Volume of cylinder: V = πr²h

- r = 5/2 = 2.5 in
- h = 10 in

→ V = 3.14 × (2.5)² × 10
→ V = 3.14 × 6.25 × 10
→ V = 3.14 × 62.5 = 196.25 in³ (full volume)

She filled 3/4:

→ 196.25 × 0.75 = 147.19 in³

✔ Answer: 147.19 cubic inches

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Problem 12:
*Erin brings a spherical container with radius 5 inches, fills with coconut flour. Each cubic inch weighs 0.35 oz. Cost $0.12 per oz.*

a) Volume of sphere:
V = (4/3)πr³

→ V = (4/3)(3.14)(5³)
→ V = (4/3)(3.14)(125)
→ V = (4/3)(392.5) = 523.333... ≈ 523.33 in³

b) Weight in ounces:
Each in³ = 0.35 oz → 523.33 × 0.35 = 183.17 oz

c) Cost: $0.12 per oz → 183.17 × 0.12 = $21.98

✔ Answers:
a) 523.33 in³
b) 183.17 oz
c) $21.98

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Problem 13:
*Ice cream cone: slant height 10 in, height 8 in.*

a) How wide is the opening at the top? → That’s the diameter of the base.

Use Pythagorean Theorem:
r² + h² = l²

→ r² + 8² = 10²
→ r² + 64 = 100
→ r² = 36 → r = 6 in → diameter = 12 in

b) If ice cream is leveled off at the top, how many cubic inches? → Volume of cone

V = (1/3)πr²h

→ V = (1/3)(3.14)(6²)(8)
→ V = (1/3)(3.14)(36)(8)
→ V = (1/3)(3.14)(288) = (1/3)(904.32) = 301.44 in³

✔ Answers:
a) 12 inches wide
b) 301.44 cubic inches

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Problem 14:
*Dixie Cup Company: changing from cone to cylinder, same radius and height. Cone holds 4 oz. How much will cylinder hold?*

Volume of cone = (1/3)πr²h
Volume of cylinder = πr²h → So cylinder holds 3 times the volume of the cone with same r and h.

→ If cone holds 4 oz, cylinder holds 4 × 3 = 12 oz

✔ Answer: 12 ounces

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Problem 15:
*Hemisphere with radius 3 inches. How many cubic inches of liquid to fill it?*

Volume of hemisphere = (1/2) × volume of sphere = (2/3)πr³

→ V = (2/3)(3.14)(3³)
→ V = (2/3)(3.14)(27)
→ V = (2/3)(84.78) = 56.52 in³

✔ Answer: 56.52 cubic inches

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✔ Final Answers Summary:

10. Height = 15.49 cm, Volume = 794.76 cm³
11. 147.19 in³
12. a) 523.33 in³, b) 183.17 oz, c) $21.98
13. a) 12 in, b) 301.44 in³
14. 12 ounces
15. 56.52 in³

Let me know if you’d like diagrams or step-by-step breakdowns for any!