Question

The total surface area of a cylinder with radius 28cm is 7392 sq. cm. Find its height and volume

Answer 1

Recall:

$\text {Surface Area of a cylinder } = 2\pi r h + 2\pi r^2$

$\text{Volume of a cylinder } = \pi r^2h$

Given:

Total surface area = $7392 \text{ cm}^2$

Radius = $28 \text{ cm}$

Find the surface area in term of h:

$\text {Surface Area of a cylinder } = 2\pi r h + 2\pi r^2$

$\text {Surface Area of a cylinder } = 2\pi (28)h + 2\pi (28)^2$

$\text {Surface Area of a cylinder } = 56\pi h + 1568\pi$

Solve h:

$\text {Surface Area of a cylinder } = 56\pi h + 1568\pi$

$\text {Surface Area of a cylinder } = 7392 \text { cm}^2$

$56\pi h + 1568\pi = 7392$

$\pi h + 28\pi = 132$

$\pi (h + 28) = 132$

$h + 28 = 42$

$h = 14 \text { cm}$

Find the volume:

$\text{Volume of a cylinder } = \pi r^2h$

$\text{Volume of a cylinder } = \pi (28)^2(14)$

$\text{Volume of a cylinder } = 34496 \text{ cm}^3$

Answer: The height is 14 cm and the volume is 34496 cm³.

Answer 2

Step-by-step explanation:

i hope you cn understand....

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