Surface Area of Cones Worksheets - Free Printable

Let’s solve each cone problem one by one. We’ll use the formula for surface area of a cone:

Surface Area = πr² + πrl

Where:
- r is the radius of the base
- l is the slant height (the diagonal side from tip to edge of base)
- Use π = 3.14 as instructed

We are given either:
- Radius and slant height → plug directly into formula
- Or radius and vertical height → we must first find slant height using Pythagoras:
l = √(r² + h²)

Then round final answer to two decimal places.

---

Problem 1:

Given: r = 16 in, h = 10 in → need slant height l

l = √(16² + 10²) = √(256 + 100) = √356 ≈ 18.87 in

SA = πr² + πrl = 3.14×16² + 3.14×16×18.87
= 3.14×256 + 3.14×301.92
= 803.84 + 948.03 ≈ 1751.87 in²

Wait — let me recalculate more precisely:

First term: 3.14 × 256 = 803.84
Second term: 16 × 18.87 = 301.92; then 3.14 × 301.92 = let's compute:

300 × 3.14 = 942
1.92 × 3.14 = 6.0288
Total second term = 942 + 6.0288 = 948.0288

Sum: 803.84 + 948.0288 = 1751.8688 → rounded to two decimals: 1751.87

✔ Correct.

---

Problem 2:

Given: diameter = 6 ft → so radius r = 3 ft
Slant height l = 10 ft (given directly)

SA = πr² + πrl = 3.14×3² + 3.14×3×10
= 3.14×9 + 3.14×30
= 28.26 + 94.2 = 122.46 ft²

✔ Done.

---

Problem 3:

Given: diameter = 4 yd → r = 2 yd
Slant height l = 6 yd (given)

SA = 3.14×2² + 3.14×2×6
= 3.14×4 + 3.14×12
= 12.56 + 37.68 = 50.24 yd²

✔ Done.

---

Problem 4:

Given: diameter = 4 yd → r = 2 yd
Slant height l = 6 yd (same as #3? Wait — diagram shows same numbers but rotated. Yes, same values.)

So SA = same as #3 → 50.24 yd²

But wait — check if it’s really same. Diagram says “4 yd” across base, “6 yd” along side → yes, same as #3.

✔ So answer is 50.24 yd²

---

Problem 5:

Given: r = 13 m, h = 7 m → need slant height

l = √(13² + 7²) = √(169 + 49) = √218 ≈ 14.7648 m

SA = 3.14×13² + 3.14×13×14.7648
First term: 3.14 × 169 = 530.66
Second term: 13 × 14.7648 = 191.9424; then 3.14 × 191.9424 ≈ ?

Compute 190 × 3.14 = 596.6
1.9424 × 3.14 ≈ 6.10 (approx) → total ≈ 602.70

Better to calculate exactly:

191.9424 × 3.14:

Breakdown:
191.9424 × 3 = 575.8272
191.9424 × 0.14 = 26.871936
Sum = 575.8272 + 26.871936 = 602.699136

Now add first term: 530.66 + 602.699136 = 1133.359136 → rounded to two decimals: 1133.36 m²

✔ Final: 1133.36

---

Problem 6:

Given: r = 15 ft, l = 20 ft (slant height given directly)

SA = 3.14×15² + 3.14×15×20
= 3.14×225 + 3.14×300
= 706.5 + 942 = 1648.50 ft²

✔ Done.

---

Problem 7:

Given: r = 6 ft, l = 9 ft (slant height given)

SA = 3.14×6² + 3.14×6×9
= 3.14×36 + 3.14×54
= 113.04 + 169.56 = 282.60 ft²

✔ Done.

---

Problem 8:

Given: r = 7 yd, l = 12 yd (slant height given)

SA = 3.14×7² + 3.14×7×12
= 3.14×49 + 3.14×84
= 153.86 + 263.76 = 417.62 yd²

✔ Done.

---

Problem 9:

Given: r = 11 in, h = 14 in → need slant height

l = √(11² + 14²) = √(121 + 196) = √317 ≈ 17.8045 in

SA = 3.14×11² + 3.14×11×17.8045
First term: 3.14 × 121 = 379.94
Second term: 11 × 17.8045 = 195.8495; then 3.14 × 195.8495 ≈ ?

Calculate:

195.8495 × 3.14
= 195.8495 × 3 = 587.5485
+ 195.8495 × 0.14 = 27.41893
Sum = 587.5485 + 27.41893 = 614.96743

Add to first term: 379.94 + 614.96743 = 994.90743 → rounded to two decimals: 994.91 in²

✔ Final: 994.91

---

## Final Answers:

1) 1751.87 in²
2) 122.46 ft²
3) 50.24 yd²
4) 50.24 yd²
5) 1133.36 m²
6) 1648.50 ft²
7) 282.60 ft²
8) 417.62 yd²
9) 994.91 in²