The sum of the altitude and the base radius of a cylinder is 63 cm. The radius is 45 as long as the altitude. Calculate the surface area volume of the cylinder?

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High School
Algebra
Pre-Algebra
Ratios, rates, proportions

Kiribatiyo2

Answered question

2022-02-10

The sum of the altitude and the base radius of a cylinder is 63 cm. The radius is

\frac{4}{5}

as long as the altitude. Calculate the surface area volume of the cylinder?

Answer & Explanation

ashuhra6e

Beginner2022-02-11Added 15 answers

Step 1
Let the altitude be h, as radius is $\frac{4}{5}$ of height, it is $\frac{4 h}{5}$ . But sum of altitude and radius is 63, hence
$h + \frac{4 h}{5} = 63$
or
$\frac{5 h}{5} + \frac{4 h}{5} = 63$
or
$\frac{9 h}{5} = 63$
Therefore
$h = 63 \times \frac{5}{9} = 7$
$⧸ 63 \times \frac{5}{⧸ 9} = 35$
Hence altitude is 35 cm and radius is
$63 - 35 = 28$ cm
Assume
$π = \frac{22}{7}$
hence surface area of cylinder given by
$π r (r + h) = \frac{22}{7} \times 28 \times 63$
$= \frac{22}{⧸ 7} \times 4$
$⧸ 28 \times 63 = 88 \times 63 = 5544$ sq.cm
Volume of cylinder is
$π r^{2} h = \frac{22}{7} \times 28 \times 28 \times 35$
$= \frac{22}{⧸ 7} \times 4$
$⧸ 28 \times 28 \times 35 = 86240$ cc.

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