Question

question 6 of 40
the surface area of the cylinder found below is 8792 cm². determine its height.
image of a cylinder with radius 20 cm and height h
a. 90 cm
b. 50 cm
c. 68 cm
d. 33 cm

Explanation:

Step1: Recall the formula for the surface area of a cylinder

The surface area \( S \) of a cylinder is given by the formula \( S = 2\pi r^2 + 2\pi r h \), where \( r \) is the radius and \( h \) is the height. From the diagram, the radius \( r = 20 \) cm, and the surface area \( S = 8792 \) \( \text{cm}^2 \).

Step2: Substitute the known values into the formula

First, calculate \( 2\pi r^2 \):
\( 2\pi(20)^2 = 2\pi\times400 = 800\pi \approx 800\times3.14 = 2512 \) \( \text{cm}^2 \)

Now, substitute \( S = 8792 \) and \( 2\pi r^2 = 2512 \) into the surface area formula:
\( 8792 = 2512 + 2\pi(20)h \)

Step3: Solve for \( h \)

First, subtract \( 2512 \) from both sides:
\( 8792 - 2512 = 2\pi(20)h \)
\( 6280 = 40\pi h \)

Now, divide both sides by \( 40\pi \) (or \( 40\times3.14 = 125.6 \)):
\( h = \frac{6280}{40\pi} \approx \frac{6280}{125.6} = 50 \) cm

Answer:

B. 50 cm