Geometry Worksheets | Volume Worksheets - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

Formulas to remember:
* Cylinder Surface Area: $2\pi r^2 + 2\pi rh$ (Area of two circles + Area of the side rectangle)
* Cone Surface Area: $\pi r^2 + \pi rl$ (Area of the base circle + Area of the curved side)
* *Note: We will use $\pi \approx 3.14159$ and round answers to the nearest hundredth.*

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1) Cylinder

* Given: Radius ($r$) = 8 ft, Height ($h$) = 12 ft
* Step 1 (Base Area): $2 \times \pi \times 8^2 = 2 \times \pi \times 64 = 128\pi$
* Step 2 (Side Area): $2 \times \pi \times 8 \times 12 = 192\pi$
* Step 3 (Total): $128\pi + 192\pi = 320\pi$
* Calculation: $320 \times 3.14159 \approx 1005.31$

2) Cone

* Given: Radius ($r$) = 4 in, Slant Height ($l$) = 6 in
* Step 1 (Base Area): $\pi \times 4^2 = 16\pi$
* Step 2 (Side Area): $\pi \times 4 \times 6 = 24\pi$
* Step 3 (Total): $16\pi + 24\pi = 40\pi$
* Calculation: $40 \times 3.14159 \approx 125.66$

3) Cylinder

* Given: Radius ($r$) = 6 yd, Height ($h$) = 8 yd
* Step 1 (Base Area): $2 \times \pi \times 6^2 = 2 \times \pi \times 36 = 72\pi$
* Step 2 (Side Area): $2 \times \pi \times 6 \times 8 = 96\pi$
* Step 3 (Total): $72\pi + 96\pi = 168\pi$
* Calculation: $168 \times 3.14159 \approx 527.79$

4) Cone

* Given: Radius ($r$) = 5 mm, Slant Height ($l$) = 13 mm
* Step 1 (Base Area): $\pi \times 5^2 = 25\pi$
* Step 2 (Side Area): $\pi \times 5 \times 13 = 65\pi$
* Step 3 (Total): $25\pi + 65\pi = 90\pi$
* Calculation: $90 \times 3.14159 \approx 282.74$

5) Cone

* Given: Radius ($r$) = 6 mm, Slant Height ($l$) = 14 mm
* Step 1 (Base Area): $\pi \times 6^2 = 36\pi$
* Step 2 (Side Area): $\pi \times 6 \times 14 = 84\pi$
* Step 3 (Total): $36\pi + 84\pi = 120\pi$
* Calculation: $120 \times 3.14159 \approx 376.99$

6) Cylinder

* Given: Radius ($r$) = 6 cm, Height ($h$) = 8 cm
* Step 1 (Base Area): $2 \times \pi \times 6^2 = 2 \times \pi \times 36 = 72\pi$
* Step 2 (Side Area): $2 \times \pi \times 6 \times 8 = 96\pi$
* Step 3 (Total): $72\pi + 96\pi = 168\pi$
* Calculation: $168 \times 3.14159 \approx 527.79$

7) Cylinder

* Given: Radius ($r$) = 7 yd, Height ($h$) = 10 yd
* Step 1 (Base Area): $2 \times \pi \times 7^2 = 2 \times \pi \times 49 = 98\pi$
* Step 2 (Side Area): $2 \times \pi \times 7 \times 10 = 140\pi$
* Step 3 (Total): $98\pi + 140\pi = 238\pi$
* Calculation: $238 \times 3.14159 \approx 747.70$

8) Cone

* Given: Radius ($r$) = 7 ft, Slant Height ($l$) = 10 ft
* Step 1 (Base Area): $\pi \times 7^2 = 49\pi$
* Step 2 (Side Area): $\pi \times 7 \times 10 = 70\pi$
* Step 3 (Total): $49\pi + 70\pi = 119\pi$
* Calculation: $119 \times 3.14159 \approx 373.85$

9) Cone

* Given: Radius ($r$) = 4 cm, Slant Height ($l$) = 6 cm
* Step 1 (Base Area): $\pi \times 4^2 = 16\pi$
* Step 2 (Side Area): $\pi \times 4 \times 6 = 24\pi$
* Step 3 (Total): $16\pi + 24\pi = 40\pi$
* Calculation: $40 \times 3.14159 \approx 125.66$

Final Answer:
1) 1005.31 ft²
2) 125.66 in²
3) 527.79 yd²
4) 282.74 mm²
5) 376.99 mm²
6) 527.79 cm²
7) 747.70 yd²
8) 373.85 ft²
9) 125.66 cm²