Surface area of sphere and hemisphere worksheet - Free Printable

Let’s solve each question one by one, step by step. We’ll use the formula for surface area of a sphere and hemisphere as needed.

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Q1. Surface area of a sphere of radius 14 cm

Formula:
Surface Area = 4πr²
Take π ≈ 22/7

So,
= 4 × (22/7) × 14 × 14
First, 14 × 14 = 196
Then, 4 × 22/7 × 196
→ 4 × 22 × 28 (because 196 ÷ 7 = 28)
→ 88 × 28 = let’s calculate:
80×28 = 2240, 8×28=224 → total = 2240 + 224 = 2464 cm²

✔ Answer: (c) 2464 cm²

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Q2. Surface area of a sphere of radius 7 cm

Again, 4πr² = 4 × (22/7) × 7 × 7
The 7 in denominator cancels with one 7 → becomes 4 × 22 × 7
= 88 × 7 = 616 cm²

✔ Answer: (b) 616 cm²

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Q3. Hollow sphere radius 2.8 m — find area available to motorcyclist

This is inner surface area of hollow sphere → same as surface area of sphere.

Radius = 2.8 m
Area = 4πr² = 4 × (22/7) × 2.8 × 2.8

First, 2.8 × 2.8 = 7.84
Now, 4 × 22/7 × 7.84
→ Let’s simplify: 7.84 ÷ 7 = 1.12
So, 4 × 22 × 1.12 = 88 × 1.12

Calculate 88 × 1.12:
88 × 1 = 88
88 × 0.12 = 10.56
Total = 88 + 10.56 = 98.56 m²

✔ Answer: (a) 98.56 m²

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Q4. Hemispherical balloon radius increases from 6 cm to 12 cm — ratio of surface areas

For a hemisphere, curved surface area = 2πr² (we assume they mean curved surface area since it's a balloon being inflated)

Initial CSA = 2π(6)² = 2π×36
Final CSA = 2π(12)² = 2π×144

Ratio = (2π×36) : (2π×144) = 36 : 144 = 1 : 4

✔ Answer: (a) 1 : 4

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Q5. Total surface area of sphere is 154 cm² — find diameter

Surface area = 4πr² = 154
So, 4 × (22/7) × r² = 154
→ (88/7) × r² = 154
Multiply both sides by 7: 88 × r² = 1078
→ r² = 1078 ÷ 88 = 12.25
→ r = √12.25 = 3.5 cm
Diameter = 2 × 3.5 = 7 cm

✔ Answer: (c) 7 cm

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Q6. Radius doubled — ratio of old surface area to new

Old SA = 4πr²
New SA = 4π(2r)² = 4π×4r² = 16πr²

Ratio old : new = 4πr² : 16πr² = 1 : 4

But note: question says “ratio of the surface area of the old is to new spheres” → so old:new = 1:4

✔ Answer: (d) 1:4

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Q7. Hemispherical bowl radius 3.5 cm — curved surface area

Curved surface area of hemisphere = 2πr²
= 2 × (22/7) × 3.5 × 3.5

3.5 × 3.5 = 12.25
2 × 22/7 × 12.25 = (44/7) × 12.25

12.25 ÷ 7 = 1.75
So, 44 × 1.75 = ?

44 × 1 = 44
44 × 0.75 = 33
Total = 44 + 33 = 77 cm²

Wait — but options have decimals. Let me recalculate precisely:

Actually, 3.5 = 7/2
So, r² = (7/2)² = 49/4
CSA = 2 × (22/7) × (49/4) = (44/7) × (49/4) = (44 × 49) / (7 × 4)

Simplify: 49 ÷ 7 = 7 → (44 × 7) / 4 = 308 / 4 = 77 cm²

But option (a) is 77 cm² — why are there decimal options? Maybe they used π = 3.14?

Try with π = 3.14:

CSA = 2 × 3.14 × (3.5)² = 2 × 3.14 × 12.25
= 6.28 × 12.25

Calculate:
6 × 12.25 = 73.5
0.28 × 12.25 = let’s see: 0.2×12.25=2.45, 0.08×12.25=0.98 → total 3.43
So 73.5 + 3.43 = 76.93 ≈ 77.0? Still close to 77.

But option (b) is 77.21 — maybe they used more precise π?

Wait — perhaps I made a mistake. Let me check again with exact fractions.

We had: 2 × (22/7) × (7/2)² = 2 × (22/7) × (49/4) = (2 × 22 × 49) / (7 × 4)

= (2156) / (28) = divide numerator and denominator by 28:

2156 ÷ 28: 28×77 = 2156 → exactly 77.

So answer should be 77 cm²

But looking at options: (a) 77 cm² — that’s correct.

Why are others there? Maybe trick? But mathematically, it’s 77.

✔ Answer: (a) 77 cm²

*(Note: If the problem meant total surface area including base, it would be 3πr² = 3×22/7×12.25 = 115.5, which isn’t an option. So definitely curved surface area.)*

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Q8. Shot-put metallic sphere radius 4.9 cm — find area

Surface area = 4πr² = 4 × (22/7) × 4.9 × 4.9

First, 4.9 × 4.9 = 24.01
Now, 4 × 22/7 × 24.01 = (88/7) × 24.01

24.01 ÷ 7 = 3.43
Then 88 × 3.43

Calculate:
80 × 3.43 = 274.4
8 × 3.43 = 27.44
Total = 274.4 + 27.44 = 301.84 cm²

✔ Answer: (c) 301.84 cm²

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Q9. Coconut radius 7 cm — cover with golden paper, cost Rs 7 per cm² — total cost?

First, surface area of sphere = 4πr² = 4 × (22/7) × 7 × 7 = 4 × 22 × 7 = 616 cm²

Cost = 616 × 7 = ?

600 × 7 = 4200
16 × 7 = 112
Total = 4200 + 112 = Rs 4312

✔ Answer: (b) Rs. 4312

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Final Answers:

Q1: (c)
Q2: (b)
Q3: (a)
Q4: (a)
Q5: (c)
Q6: (d)
Q7: (a)
Q8: (c)
Q9: (b)

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Final Answer:
Q1: (c) 2464 cm²
Q2: (b) 616 cm²
Q3: (a) 98.56 m²
Q4: (a) 1 : 4
Q5: (c) 7 cm
Q6: (d) 1:4
Q7: (a) 77 cm²
Q8: (c) 301.84 cm²
Q9: (b) Rs. 4312