surface area of a cone 1-26 online exercise for - Free Printable

Let’s solve each cone surface area problem one by one.

We’ll use the formula for surface area of a cone:

> Surface Area = π × r × (r + l)
> where:
> - r = radius of the base
> - l = slant height (the diagonal side from tip to edge of base)
> - π = 3.14 (as given)

Sometimes, we’re given the diameter instead of radius — remember:
> radius = diameter ÷ 2

Also, if we’re given the vertical height and radius, we may need to find the slant height using the Pythagorean theorem:
> l = √(r² + h²)

But in this worksheet, most problems give us either:
- radius and slant height → plug into formula directly
- or diameter and slant height → convert diameter to radius first
- or radius and vertical height → calculate slant height first

Let’s go step by step.

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Problem 1:

Given:
- Slant height (l) = 7 in
- Radius (r) = 2 in

SA = 3.14 × 2 × (2 + 7)
= 3.14 × 2 × 9
= 6.28 × 9
= 56.52 in²

✔ Final Answer for #1: 56.52

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Problem 2:

Given:
- Diameter = 9 ft → so radius r = 9 ÷ 2 = 4.5 ft
- Slant height l = 11 ft

SA = 3.14 × 4.5 × (4.5 + 11)
= 3.14 × 4.5 × 15.5
First: 4.5 × 15.5 = let’s compute:
4.5 × 15 = 67.5
4.5 × 0.5 = 2.25
Total = 67.5 + 2.25 = 69.75

Now: 3.14 × 69.75
Break it down:
3 × 69.75 = 209.25
0.14 × 69.75 = ?
0.1 × 69.75 = 6.975
0.04 × 69.75 = 2.79
So 6.975 + 2.79 = 9.765
Total SA = 209.25 + 9.765 = 219.015

Round to two decimals → 219.02 ft²

✔ Final Answer for #2: 219.02

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Problem 3:

Given:
- Diameter = 5 yd → radius r = 5 ÷ 2 = 2.5 yd
- Slant height l = 10 yd

SA = 3.14 × 2.5 × (2.5 + 10)
= 3.14 × 2.5 × 12.5
First: 2.5 × 12.5 = 31.25
Then: 3.14 × 31.25
Compute:
3 × 31.25 = 93.75
0.14 × 31.25 = ?
0.1 × 31.25 = 3.125
0.04 × 31.25 = 1.25
Sum: 3.125 + 1.25 = 4.375
Total: 93.75 + 4.375 = 98.125

Round to two decimals → 98.13 yd²

✔ Final Answer for #3: 98.13

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Problem 4:

Given:
- Diameter = 11 ft → radius r = 11 ÷ 2 = 5.5 ft
- Slant height l = 15 ft

SA = 3.14 × 5.5 × (5.5 + 15)
= 3.14 × 5.5 × 20.5
First: 5.5 × 20.5
5 × 20.5 = 102.5
0.5 × 20.5 = 10.25
Total = 102.5 + 10.25 = 112.75

Now: 3.14 × 112.75
3 × 112.75 = 338.25
0.14 × 112.75 = ?
0.1 × 112.75 = 11.275
0.04 × 112.75 = 4.51
Sum: 11.275 + 4.51 = 15.785
Total: 338.25 + 15.785 = 354.035

Round → 354.04 ft²

✔ Final Answer for #4: 354.04

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Problem 5:

Given:
- Radius r = 10 yd
- Slant height l = 20 yd

SA = 3.14 × 10 × (10 + 20)
= 3.14 × 10 × 30
= 3.14 × 300
= 942.00 yd²

✔ Final Answer for #5: 942.00

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Problem 6:

Given:
- Radius r = 3 in
- Vertical height h = 4 in → NOT slant height! Need to find slant height.

Use Pythagoras:
l = √(r² + h²) = √(3² + 4²) = √(9 + 16) = √25 = 5 in

Now SA = 3.14 × 3 × (3 + 5)
= 3.14 × 3 × 8
= 3.14 × 24
= 75.36 in²

✔ Final Answer for #6: 75.36

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Problem 7:

Given:
- Radius r = 3 yd
- Slant height l = 19 yd

SA = 3.14 × 3 × (3 + 19)
= 3.14 × 3 × 22
= 3.14 × 66
= 207.24 yd²

✔ Final Answer for #7: 207.24

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Problem 8:

Given:
- Radius r = 8 in
- Vertical height h = 14 in → need slant height

l = √(8² + 14²) = √(64 + 196) = √260 ≈ ?

√260: Let’s approximate.
16² = 256 → so √260 ≈ 16.12 (since 16.12² = 259.8544 — close enough)

Actually, let’s compute more precisely:

16.1² = 259.21
16.12² = (16 + 0.12)² = 256 + 2×16×0.12 + 0.0144 = 256 + 3.84 + 0.0144 = 259.8544
16.13² = 16.12² + 2×16.12×0.01 + 0.0001 ≈ 259.8544 + 0.3224 + 0.0001 = 260.1769 → too big

So √260 ≈ 16.1245 — but since we’re rounding final answer to 2 decimals, maybe keep extra digits during calc.

But let’s use exact value for now: l = √260

SA = 3.14 × 8 × (8 + √260)

Wait — better to compute numerically:

l = √(64 + 196) = √260 ≈ 16.124515...

So SA = 3.14 × 8 × (8 + 16.124515)
= 3.14 × 8 × 24.124515
First: 8 × 24.124515 = 192.99612
Then: 3.14 × 192.99612 ≈ ?

3 × 192.99612 = 578.98836
0.14 × 192.99612 ≈ 27.0194568
Total ≈ 578.98836 + 27.0194568 = 606.0078168

Round to two decimals → 606.01 in²

✔ Final Answer for #8: 606.01

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Problem 9:

Given:
- Diameter = 8 ft → radius r = 4 ft
- Slant height l = 12 ft

SA = 3.14 × 4 × (4 + 12)
= 3.14 × 4 × 16
= 3.14 × 64
= 200.96 ft²

✔ Final Answer for #9: 200.96

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Final Answers:

1) 56.52
2) 219.02
3) 98.13
4) 354.04
5) 942.00
6) 75.36
7) 207.24
8) 606.01
9) 200.96