To find the surface area of each figure, we use specific formulas for cylinders and cones.
Formulas:
*
Cylinder Surface Area: $SA = 2\pi r^2 + 2\pi rh$
* $r$ = radius, $h$ = height
*
Cone Surface Area: $SA = \pi r^2 + \pi rl$
* $r$ = radius, $l$ = slant height
Let's calculate the surface area for each problem step-by-step.
1) Cylinder
* Radius ($r$) = 8 ft
* Height ($h$) = 12 ft
* $SA = 2\pi(8)^2 + 2\pi(8)(12)$
* $SA = 2\pi(64) + 2\pi(96)$
* $SA = 128\pi + 192\pi = 320\pi$
* $320 \times 3.14159 \approx 1005.31$ sq ft
2) Cone
* Radius ($r$) = 4 in
* Slant Height ($l$) = 6 in
* $SA = \pi(4)^2 + \pi(4)(6)$
* $SA = 16\pi + 24\pi = 40\pi$
* $40 \times 3.14159 \approx 125.66$ sq in
3) Cylinder
* Radius ($r$) = 6 yd
* Height ($h$) = 8 yd
* $SA = 2\pi(6)^2 + 2\pi(6)(8)$
* $SA = 2\pi(36) + 2\pi(48)$
* $SA = 72\pi + 96\pi = 168\pi$
* $168 \times 3.14159 \approx 527.79$ sq yd
4) Cone
* Radius ($r$) = 5 mm
* Slant Height ($l$) = 13 mm
* $SA = \pi(5)^2 + \pi(5)(13)$
* $SA = 25\pi + 65\pi = 90\pi$
* $90 \times 3.14159 \approx 282.74$ sq mm
5) Cone
* Radius ($r$) = 6 mm
* Slant Height ($l$) = 14 mm
* $SA = \pi(6)^2 + \pi(6)(14)$
* $SA = 36\pi + 84\pi = 120\pi$
* $120 \times 3.14159 \approx 376.99$ sq mm
6) Cylinder
* Radius ($r$) = 6 cm
* Height ($h$) = 8 cm
* $SA = 2\pi(6)^2 + 2\pi(6)(8)$
* $SA = 2\pi(36) + 2\pi(48)$
* $SA = 72\pi + 96\pi = 168\pi$
* $168 \times 3.14159 \approx 527.79$ sq cm
7) Cylinder
* Radius ($r$) = 7 yd
* Height ($h$) = 10 yd
* $SA = 2\pi(7)^2 + 2\pi(7)(10)$
* $SA = 2\pi(49) + 2\pi(70)$
* $SA = 98\pi + 140\pi = 238\pi$
* $238 \times 3.14159 \approx 747.70$ sq yd
8) Cone
* Radius ($r$) = 7 ft
* Slant Height ($l$) = 10 ft
* $SA = \pi(7)^2 + \pi(7)(10)$
* $SA = 49\pi + 70\pi = 119\pi$
* $119 \times 3.14159 \approx 373.85$ sq ft
9) Cone
* Radius ($r$) = 4 cm
* Slant Height ($l$) = 6 cm
* $SA = \pi(4)^2 + \pi(4)(6)$
* $SA = 16\pi + 24\pi = 40\pi$
* $40 \times 3.14159 \approx 125.66$ sq cm
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
Parent Tip: Review the logic above to help your child master the concept of surface area worksheet.
