Geometry Worksheets | Volume Worksheets - Free Printable
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Step-by-step solution for: Geometry Worksheets | Volume Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Geometry Worksheets | Volume Worksheets
Explanation:
We need to find the surface area of each cylinder and cone. Let’s recall the formulas:
- Cylinder surface area = $2\pi r^2 + 2\pi r h = 2\pi r(r + h)$
(Two circular bases + lateral surface)
- Cone surface area = $\pi r^2 + \pi r \ell = \pi r(r + \ell)$
(One circular base + lateral surface, where $\ell$ is the slant height)
⚠️ Important: For cones, we are given the slant height ($\ell$) in all cases — look at the diagram labels (e.g., “13 mm” on the side of the cone). So we can use it directly.
Let’s solve each one carefully, rounding to the nearest hundredth if needed.
---
1) Cylinder:
Diameter = 8 ft → radius $r = 4$ ft
Height $h = 12$ ft
Surface area = $2\pi r(r + h) = 2\pi(4)(4 + 12) = 2\pi(4)(16) = 128\pi$
$128\pi \approx 128 \times 3.1416 = 402.1239 \approx \mathbf{402.12}$ ft²
✔ Check: Yes, using formula correctly.
---
2) Cone:
Radius $r = 4$ in
Slant height $\ell = 6$ in
Surface area = $\pi r(r + \ell) = \pi(4)(4 + 6) = \pi(4)(10) = 40\pi$
$40\pi \approx 40 \times 3.1416 = 125.6637 \approx \mathbf{125.66}$ in²
✔ Correct.
---
3) Cylinder:
Diameter = 6 yd → radius $r = 3$ yd
Height $h = 8$ yd
Surface area = $2\pi r(r + h) = 2\pi(3)(3 + 8) = 2\pi(3)(11) = 66\pi$
$66\pi \approx 66 \times 3.1416 = 207.3456 \approx \mathbf{207.35}$ yd²
✔ Good.
---
4) Cone:
Radius $r = 5$ mm
Slant height $\ell = 13$ mm
Surface area = $\pi r(r + \ell) = \pi(5)(5 + 13) = \pi(5)(18) = 90\pi$
$90\pi \approx 90 \times 3.1416 = 282.7433 \approx \mathbf{282.74}$ mm²
✔ Correct.
---
5) Cone:
Radius $r = 6$ mm
Slant height $\ell = 14$ mm
Surface area = $\pi(6)(6 + 14) = \pi(6)(20) = 120\pi$
$120\pi \approx 120 \times 3.1416 = 376.9911 \approx \mathbf{376.99}$ mm²
✔ Good.
---
6) Cylinder:
Diameter = 6 cm → radius $r = 3$ cm
Height $h = 8$ cm
Surface area = $2\pi(3)(3 + 8) = 2\pi(3)(11) = 66\pi \approx 207.35$ cm²
Same as #3 → $\mathbf{207.35}$ cm²
✔ Yes.
---
7) Cylinder:
Diameter = 7 yd → radius $r = 3.5$ yd
Height $h = 10$ yd
Surface area = $2\pi r(r + h) = 2\pi(3.5)(3.5 + 10) = 2\pi(3.5)(13.5)$
First compute: $3.5 \times 13.5 = 47.25$
Then $2 \times 47.25 = 94.5$
So surface area = $94.5\pi \approx 94.5 \times 3.1416 = 296.8812 \approx \mathbf{296.88}$ yd²
✔ Double-checked.
---
8) Cone:
Radius $r = 7$ ft
Slant height $\ell = 10$ ft
Surface area = $\pi(7)(7 + 10) = \pi(7)(17) = 119\pi$
$119\pi \approx 119 \times 3.1416 = 373.8504 \approx \mathbf{373.85}$ ft²
✔ Correct.
---
9) Cone:
Radius $r = 4$ cm
Slant height $\ell = 6$ cm
Surface area = $\pi(4)(4 + 6) = \pi(4)(10) = 40\pi \approx 125.66$ cm²
Same as #2 → $\mathbf{125.66}$ cm²
✔ All done.
Now list final answers in order:
1) 402.12
2) 125.66
3) 207.35
4) 282.74
5) 376.99
6) 207.35
7) 296.88
8) 373.85
9) 125.66
Final Answer:
402.12, 125.66, 207.35, 282.74, 376.99, 207.35, 296.88, 373.85, 125.66
We need to find the surface area of each cylinder and cone. Let’s recall the formulas:
- Cylinder surface area = $2\pi r^2 + 2\pi r h = 2\pi r(r + h)$
(Two circular bases + lateral surface)
- Cone surface area = $\pi r^2 + \pi r \ell = \pi r(r + \ell)$
(One circular base + lateral surface, where $\ell$ is the slant height)
⚠️ Important: For cones, we are given the slant height ($\ell$) in all cases — look at the diagram labels (e.g., “13 mm” on the side of the cone). So we can use it directly.
Let’s solve each one carefully, rounding to the nearest hundredth if needed.
---
1) Cylinder:
Diameter = 8 ft → radius $r = 4$ ft
Height $h = 12$ ft
Surface area = $2\pi r(r + h) = 2\pi(4)(4 + 12) = 2\pi(4)(16) = 128\pi$
$128\pi \approx 128 \times 3.1416 = 402.1239 \approx \mathbf{402.12}$ ft²
✔ Check: Yes, using formula correctly.
---
2) Cone:
Radius $r = 4$ in
Slant height $\ell = 6$ in
Surface area = $\pi r(r + \ell) = \pi(4)(4 + 6) = \pi(4)(10) = 40\pi$
$40\pi \approx 40 \times 3.1416 = 125.6637 \approx \mathbf{125.66}$ in²
✔ Correct.
---
3) Cylinder:
Diameter = 6 yd → radius $r = 3$ yd
Height $h = 8$ yd
Surface area = $2\pi r(r + h) = 2\pi(3)(3 + 8) = 2\pi(3)(11) = 66\pi$
$66\pi \approx 66 \times 3.1416 = 207.3456 \approx \mathbf{207.35}$ yd²
✔ Good.
---
4) Cone:
Radius $r = 5$ mm
Slant height $\ell = 13$ mm
Surface area = $\pi r(r + \ell) = \pi(5)(5 + 13) = \pi(5)(18) = 90\pi$
$90\pi \approx 90 \times 3.1416 = 282.7433 \approx \mathbf{282.74}$ mm²
✔ Correct.
---
5) Cone:
Radius $r = 6$ mm
Slant height $\ell = 14$ mm
Surface area = $\pi(6)(6 + 14) = \pi(6)(20) = 120\pi$
$120\pi \approx 120 \times 3.1416 = 376.9911 \approx \mathbf{376.99}$ mm²
✔ Good.
---
6) Cylinder:
Diameter = 6 cm → radius $r = 3$ cm
Height $h = 8$ cm
Surface area = $2\pi(3)(3 + 8) = 2\pi(3)(11) = 66\pi \approx 207.35$ cm²
Same as #3 → $\mathbf{207.35}$ cm²
✔ Yes.
---
7) Cylinder:
Diameter = 7 yd → radius $r = 3.5$ yd
Height $h = 10$ yd
Surface area = $2\pi r(r + h) = 2\pi(3.5)(3.5 + 10) = 2\pi(3.5)(13.5)$
First compute: $3.5 \times 13.5 = 47.25$
Then $2 \times 47.25 = 94.5$
So surface area = $94.5\pi \approx 94.5 \times 3.1416 = 296.8812 \approx \mathbf{296.88}$ yd²
✔ Double-checked.
---
8) Cone:
Radius $r = 7$ ft
Slant height $\ell = 10$ ft
Surface area = $\pi(7)(7 + 10) = \pi(7)(17) = 119\pi$
$119\pi \approx 119 \times 3.1416 = 373.8504 \approx \mathbf{373.85}$ ft²
✔ Correct.
---
9) Cone:
Radius $r = 4$ cm
Slant height $\ell = 6$ cm
Surface area = $\pi(4)(4 + 6) = \pi(4)(10) = 40\pi \approx 125.66$ cm²
Same as #2 → $\mathbf{125.66}$ cm²
✔ All done.
Now list final answers in order:
1) 402.12
2) 125.66
3) 207.35
4) 282.74
5) 376.99
6) 207.35
7) 296.88
8) 373.85
9) 125.66
Final Answer:
402.12, 125.66, 207.35, 282.74, 376.99, 207.35, 296.88, 373.85, 125.66
Parent Tip: Review the logic above to help your child master the concept of surface area and volume worksheet with answers.
