Question

I'd the total surface area of a cylinder is 450 cm sq. and its base circumference is 50 cm then what will be the sum of its height and radius​

Answer 1

The sum of its height and radius is 9 cm.

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Let's understand a few concepts:

To calculate the total surface area of a cylinder we will use the following formula:

$\boxed{\bold{Total\:surface\:area\:of\:a\:cylinder = C.S.A + Area\:of\:top\:face + Area \:of\:bottom\:face}}$

$\boxed{\bold{Total\:surface\:area\:of\:a\:cylinder = 2\pi rh + \pi r^2 + \pi r^2 = 2\pi rh + 2\pi r^2 = 2\pi r (h + r)}}$

Also, the base circumference of a cylinder is equal to the circumference of a circle i.e.,

$\boxed{\bold{Circumference \:of\:a\:circle =2 \pi r}}$

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Let's solve the given problem:

The total surface area of the cylinder = 450 cm²

The base circumference of the cylinder = 50 cm

Let "r" cm and "h" cm represent the radius and height of the given cylinder respectively.

Therefore, we can form the equation as,

$2\pi r (h + r) = 450$

$\implies (Circumference \:of\:the \:base\:of\:cylinder)\times (h + r) = 450$

$\implies 50\times (h + r) = 450$

$\implies (h + r) = \frac{450}{50}$

$\implies (h + r) = \frac{45}{5}$

$\implies \bold{(h + r) =9\:cm}$

Thus, the sum of the height and radius​ of the given cylinder is 9 cm.

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