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

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

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

> Surface Area = π × r² + π × r × l

Where:
- r = radius of the base
- l = slant height (the diagonal side from tip to edge of base)
- We are told to use π = 3.14
- Round final answer to two decimal places

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Problem 1:

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

SA = 3.14 × (2)² + 3.14 × 2 × 7
= 3.14 × 4 + 3.14 × 14
= 12.56 + 43.96
= 56.52 in²

✔ Check: 4×3.14=12.56, 14×3.14=43.96 → sum is 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)² + 3.14 × 4.5 × 11
First, 4.5² = 20.25
→ 3.14 × 20.25 = let’s calculate:
3 × 20.25 = 60.75, 0.14 × 20.25 ≈ 2.835 → total ≈ 63.585
Better to do exact:
3.14 × 20.25 = 63.585

Now second part: 3.14 × 4.5 × 11
First, 4.5 × 11 = 49.5
Then 3.14 × 49.5 = ?

Break it down:
3 × 49.5 = 148.5
0.14 × 49.5 = 6.93
Total = 148.5 + 6.93 = 155.43

Now add both parts:
63.585 + 155.43 = 219.015 → round to 219.02 ft²

✔ Double-check with calculator-style steps:
(3.14 * 20.25) = 63.585
(3.14 * 4.5 * 11) = 3.14 * 49.5 = 155.43
Sum: 63.585 + 155.43 = 219.015 → rounded to 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 + 3.14 × 2.5 × 10
2.5² = 6.25
3.14 × 6.25 = 19.625
3.14 × 2.5 × 10 = 3.14 × 25 = 78.5
Add: 19.625 + 78.5 = 98.125 → round to 98.13 yd²

✔ Correct.

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Problem 4:

Given:
Diameter = 11 ft → r = 5.5 ft
Slant height l = 15 ft

SA = 3.14 × (5.5)² + 3.14 × 5.5 × 15
5.5² = 30.25
3.14 × 30.25 = let’s compute:
3 × 30.25 = 90.75
0.14 × 30.25 = 4.235
Total = 94.985

Second part: 3.14 × 5.5 × 15
First, 5.5 × 15 = 82.5
3.14 × 82.5 = ?

3 × 82.5 = 247.5
0.14 × 82.5 = 11.55
Total = 259.05

Add: 94.985 + 259.05 = 354.035 → round to 354.04 ft²

✔ Verified.

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Problem 5:

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

SA = 3.14 × (10)² + 3.14 × 10 × 20
= 3.14 × 100 + 3.14 × 200
= 314 + 628
= 942.00 yd²

✔ Simple and clean.

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Problem 6:

This one gives us height and radius, not slant height!

Given:
Height h = 4 in
Radius r = 3 in

We need to find slant height (l) first using Pythagoras:

> l = √(r² + h²) = √(3² + 4²) = √(9 + 16) = √25 = 5 in

Now plug into SA formula:

SA = 3.14 × (3)² + 3.14 × 3 × 5
= 3.14 × 9 + 3.14 × 15
= 28.26 + 47.10
= 75.36 in²

✔ Classic 3-4-5 triangle — correct.

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Problem 7:

Given:
Slant height l = 19 yd
Radius r = 13 yd? Wait — look at diagram: the dashed line labeled “13 yd” goes from center to edge → that’s radius. The other label “19 yd” is along the side → that’s slant height.

So r = 13 yd, l = 19 yd

SA = 3.14 × (13)² + 3.14 × 13 × 19
13² = 169
3.14 × 169 = ?

Calculate:
3 × 169 = 507
0.14 × 169 = 23.66
Total = 530.66

Second part: 3.14 × 13 × 19
First, 13 × 19 = 247
Then 3.14 × 247 = ?

3 × 247 = 741
0.14 × 247 = 34.58
Total = 775.58

Add: 530.66 + 775.58 = 1306.24 yd²

✔ Confirmed.

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Problem 8:

Again, we’re given height and radius, not slant height.

Given:
Height h = 14 in
Radius r = 8 in

Find slant height:
l = √(8² + 14²) = √(64 + 196) = √260

√260 ≈ ? Let’s approximate:

16² = 256 → so √260 ≈ 16.1245...

Use 16.12 for calculation (we'll keep more digits if needed).

But better to compute exactly as possible.

Actually, let’s compute numerically:

√260 = √(4×65) = 2√65 ≈ 2 × 8.0623 = 16.1246

So l ≈ 16.1246 in

Now SA = 3.14 × (8)² + 3.14 × 8 × 16.1246
= 3.14 × 64 + 3.14 × 8 × 16.1246

First term: 3.14 × 64 = 200.96

Second term: 8 × 16.1246 = 128.9968
Then 3.14 × 128.9968 ≈ ?

Compute:
3 × 128.9968 = 386.9904
0.14 × 128.9968 ≈ 18.059552
Total ≈ 405.049952

Now add: 200.96 + 405.049952 ≈ 606.009952 → round to 606.01 in²

Wait — let me double-check this because rounding early might cause error.

Alternative approach: Use exact value until end.

l = √(8² + 14²) = √(64 + 196) = √260

SA = πr(r + l) = 3.14 × 8 × (8 + √260)

Compute inside: 8 + √260 ≈ 8 + 16.1245155 = 24.1245155

Then 8 × 24.1245155 = 192.996124

Then 3.14 × 192.996124 ≈ ?

3 × 192.996124 = 578.988372
0.14 × 192.996124 ≈ 27.01945736
Total ≈ 606.007829 → still rounds to 606.01 in²

✔ So answer is 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)² + 3.14 × 4 × 12
= 3.14 × 16 + 3.14 × 48
= 50.24 + 150.72
= 200.96 ft²

✔ Straightforward.

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## Final Answers:

1) 56.52 in²
2) 219.02 ft²
3) 98.13 yd²
4) 354.04 ft²
5) 942.00 yd²
6) 75.36 in²
7) 1306.24 yd²
8) 606.01 in²
9) 200.96 ft²

──────────────────────────────────────

Final Answer:
1) 56.52
2) 219.02
3) 98.13
4) 354.04
5) 942.00
6) 75.36
7) 1306.24
8) 606.01
9) 200.96