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The formula for the surface area of a cylinder is 
2pi r(r+h) where 
r is the radius of the cylinder's base and 
h is its height.
A certain pole has a cylinder-like shape, where the base's radius is 10 centimeters and the height is 2 meters.
What calculation will give us the estimated surface area of the pole in square centimeters?
Choose 1 answer:
(A) 
2pi*10*12
(B) 
2pi*10*210
(C) 
2pi*0.01*2.01
(D) 
2pi*0.01*200.01

The formula for the surface area of a cylinder is \newline2πr(r+h)2\pi r(r+h) where \newlinerr is the radius of the cylinder's base and \newlinehh is its height.\newlineA certain pole has a cylinder-like shape, where the base's radius is 1010 centimeters and the height is 22 meters.\newlineWhat calculation will give us the estimated surface area of the pole in square centimeters?\newlineChoose 11 answer:\newline(A) 2π10122\pi \cdot 10 \cdot 12\newline(B) 2π102102\pi \cdot 10 \cdot 210\newline(C) 2π0.012.012\pi \cdot 0.01 \cdot 2.01\newline(D) 2π0.01200.012\pi \cdot 0.01 \cdot 200.01

Full solution

Q. The formula for the surface area of a cylinder is \newline2πr(r+h)2\pi r(r+h) where \newlinerr is the radius of the cylinder's base and \newlinehh is its height.\newlineA certain pole has a cylinder-like shape, where the base's radius is 1010 centimeters and the height is 22 meters.\newlineWhat calculation will give us the estimated surface area of the pole in square centimeters?\newlineChoose 11 answer:\newline(A) 2π10122\pi \cdot 10 \cdot 12\newline(B) 2π102102\pi \cdot 10 \cdot 210\newline(C) 2π0.012.012\pi \cdot 0.01 \cdot 2.01\newline(D) 2π0.01200.012\pi \cdot 0.01 \cdot 200.01
  1. Identify Given Values: Identify the given values for the radius and height of the cylinder. The radius rr is 1010 centimeters, and the height hh is given in meters, so it needs to be converted to centimeters.\newlineHeight in meters = 22 m\newlineConvert meters to centimeters: 11 m = 100100 cm\newlineHeight in centimeters = 22 m * 100100 cm/m = 200200 cm
  2. Write Formula: Write down the formula for the surface area of a cylinder: Surface Area = 2πr(r+h)2 \pi r (r + h).
  3. Substitute Values: Substitute the given values into the formula: Surface Area =2×π×10cm×(10cm+200cm)= 2 \times \pi \times 10 \, \text{cm} \times (10 \, \text{cm} + 200 \, \text{cm}).
  4. Simplify Expression: Simplify the expression inside the parentheses: 10cm+200cm=210cm.10\,\text{cm} + 200\,\text{cm} = 210\,\text{cm}.
  5. Calculate Surface Area: Now, substitute the simplified expression back into the formula: Surface Area = 2×π×10cm×210cm2 \times \pi \times 10 \, \text{cm} \times 210 \, \text{cm}.
  6. Identify Correct Answer: Identify the correct answer from the given options. The calculation that matches our formula is (B) 2π102102\pi\cdot 10\cdot 210.

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