Question

The sum of the radius and the height of a cylinder is 37 cm. If its total surface area
is 1628 cm?, find its height. Also, find its volume.
​

Answer 1

Let the radius of a cylinder be r and the height be h.

Given:

r+h=37 cm.................. (1)

Total Surface Area of a cylinder=1628 cm².

To Find:

Height of a cylinder(h) =?

Volume=?

Solution:

Total Surface Area of a cylinder=2πr(r+h).

1628=2×22/7×r(37).......(from(1))

1628×7/22×2=37r

259=37r

r=259/37

r=7 cm.

Substituting the value of r in (1) we get,

r+h=37........... (1)

7+h=37

h=37-7

h=30 cm

Answer 2

Answer:

The height of the cylinder is 30 cm.

The volume of the cylinder is 4620 cm³.

Step-by-step-explanation:

We have given that the sum of radius and height of a cylinder is 37 cm.

Also, total surface area of cylinder is 1628 cm² i. e.

$\sf\:TSA_{cylinder}\:=\:1628\:cm^{2}$.

We have to find height and volume of the cylinder.

From the given information,

$\sf\:r\:+\:h\:=\:37\:\:\:-\:-\:-\:(\:1\:)$

We know that,

$\pink{\sf\:TSA_{cylinder}\:=\:2\:\pi\:r\:(\:r\:+\:h\:)}\\\\\implies\sf\:1628\:=\:2\:\times\:\frac{22}{7}\:\times\:r\:\times\:37\:\:-\:-\:[\:From\:(\:1\:)\:]\\\\\implies\sf\:\dfrac{\cancel{1628}\:\times\:7}{2\:\times\:\cancel{22}\:\times\:37}\:=\:r\\\\\implies\sf\:r\:=\:\dfrac{\cancel{74}\:\times\:7}{2\:\times\:\cancel{37}}\\\\\implies\sf\:r\:=\:\dfrac{\cancel{2}\:\times\:7}{\cancel2}\\\\\implies\boxed{\red{\sf\:r\:=\:7\:cm}}$

Now, by substituting r = 7 in equation ( 1 ), we get,

$\sf\:r\:+\:h\:=\:37\:\:\:-\:-\:-\:(\:1\:)\\\\\implies\sf\:7\:+\:h\:=\:37\\\\\implies\sf\:h\:=\:37\:-\:7\\\\\implies\boxed{\red{\sf\:h\:=\:30\:cm}}$

Now, we know that,

$\pink{\sf\:V_{cylinder}\:=\:\pi\:r^{2}\:h}\\\\\implies\sf\:V_{cylinder}\:=\:\frac{22}{7}\:\times\:7^{2}\:\times\:30\\\\\implies\sf\:V_{cylinder}\:=\:\frac{22}{\cancel7}\:\times\:\cancel{7}\:\times\:7\:\times\:30\\\\\implies\sf\:V_{cylinder}\:=\:22\:\times\:7\:\times\:30\\\\\implies\sf\:V_{cylinder}\:=\:154\:\times\:30\\\\\implies\boxed{\red{\sf\:V_{cylinder}\:=\:4620\:cm^{3}}}$