A cylinder has a surface area (including ends) of 180.6 sq cm and a diameter of 5 cm. What is the height?

A cylinder has a surface area (including ends) of 180.6 sq cm and a diameter of 5 cm. What is the height?

• A. 9.0 cm
• B. 28.3 cm
• C. 11.5 cm
• D. 5.0 cm

Answer: (A)

To find the height of the cylinder given its surface area and diameter, we begin by recalling the formula for the total surface area (A) of a cylinder: \[ A = 2\pi r^2 + 2\pi rh \] Here, \( r \) is the radius, \( h \) is the height, and \( \pi \) is a constant approximately equal to 3.14. Given a diameter of 5 cm, we can calculate the radius: \[ r = \frac{diameter}{2} = \frac{5 \, cm}{2} = 2.5 \, cm \] Now we substitute the known values into the surface area formula. We are given the total surface area being 180.6 sq cm: \[ 180.6 = 2\pi (2.5^2) + 2\pi (2.5)h \] Calculating the area of the circular ends: \[ 2\pi (2.5^2) = 2\pi (6.25) = 12.5\pi \approx 39.27 \, sq \, cm \] Now we substitute this into our equation: \[

To find the height of the cylinder given its surface area and diameter, we begin by recalling the formula for the total surface area (A) of a cylinder:

[ A = 2\pi r^2 + 2\pi rh ]

Here, ( r ) is the radius, ( h ) is the height, and ( \pi ) is a constant approximately equal to 3.14. Given a diameter of 5 cm, we can calculate the radius:

[ r = \frac{diameter}{2} = \frac{5 , cm}{2} = 2.5 , cm ]

Now we substitute the known values into the surface area formula. We are given the total surface area being 180.6 sq cm:

[ 180.6 = 2\pi (2.5^2) + 2\pi (2.5)h ]

Calculating the area of the circular ends:

[ 2\pi (2.5^2) = 2\pi (6.25) = 12.5\pi \approx 39.27 , sq , cm ]

Now we substitute this into our equation:

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