Let’s solve each volume step by step.
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1. Sphere (radius = 7 cm)
Formula for volume of a sphere:
> V = (4/3)πr³
Plug in r = 7:
V = (4/3) × π × 7³
7³ = 343
So, V = (4/3) × π × 343
= (1372/3)π cm³ → This is the
exact form
Now calculate decimal value:
1372 ÷ 3 ≈ 457.333...
Multiply by π ≈ 3.14159265
457.333... × 3.14159265 ≈ 1436.755...
Rounded to 2 decimal places:
1436.76 cm³
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2. Cone (radius = 4 cm, height = 13 cm)
Formula for volume of a cone:
> V = (1/3)πr²h
Plug in r = 4, h = 13:
V = (1/3) × π × 4² × 13
4² = 16
So, V = (1/3) × π × 16 × 13
16 × 13 = 208
V = (208/3)π cm³ → This is the
exact form
Decimal value:
208 ÷ 3 ≈ 69.333...
× π ≈ 69.333... × 3.14159265 ≈ 217.817...
Rounded to 2 decimal places:
217.82 cm³
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3. Square-based pyramid (base side = 60 cm, height = 30 cm)
Formula for volume of a pyramid:
> V = (1/3) × base area × height
Base is a square: area = side² = 60 × 60 = 3600 cm²
Height = 30 cm
V = (1/3) × 3600 × 30
First, 3600 × 30 = 108,000
Then, 108,000 ÷ 3 = 36,000 cm³
No rounding needed — it’s a whole number.
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Final Answer:
Sphere: (a) $\frac{1372}{3}\pi$ cm³, (b) 1436.76 cm³
Cone: (a) $\frac{208}{3}\pi$ cm³, (b) 217.82 cm³
Square-based pyramid: 36000 cm³
Parent Tip: Review the logic above to help your child master the concept of volume of pyramids and cones worksheet answers.
