Question

2. The radius of a cylinder is 5 cm. If its total surface area is 600 cm?, find its height.
3. The volume of a cylinder is 924 m and its curved surface area is 264 mFind:
(i) its radius; (ii) its height​

Answer 1

2. Given:

1. Radius of a cylinder =5 cm.

2.Total surface Area=600 cm².

To Find:

Height(h) =?

Solution:

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

600=2×π×5(5+h)

600=10π(5+h)

600/10=π(5+h)

60=22/7(5+h)

60×7/22=5+h

30×7/11=5+h

210/11=5+h

19.09=5+h

19.09-5=h

h=14.09 cm

3.Given:

Volume of a cylinder=924 m³.

Curved Surface Area=264 m²

To Find:

(i) Radius(r) =?

(ii) Height (h) =?

Solution:

Volume of a cylinder=πr²h.

924=πr²h

924=22/7 ×r²h

924×7/22=r²h

294=r²h........(1)

Curved Surface Area=2πrh....

264=2×22/7×rh

264×7/22×2=rh

42=rh

h=42/r..........(2)

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

294=r²×42/r

294=42r²/r

294=42r

r=294/42

r=7 m

Now, substituting the value of r in (2) we get,

h=42/7

h=6m

HOPE IT HELP YOU!

Answer 2

Answer:

2.

The height of the cylinder is 14.09 cm.

3.

( i ) The radius of cylinder is 7 m.

( ii ) The height of the cylinder is 6 m.

Step-by-step-explanation:

2.

We have given that radius of the cylinder is

5 cm.

Also, total surface area of cylinder is

600 cm².

We have to find height of the cylinder.

We know that,

$\pink{\sf\:TSA_{cylinder}\:=\:2\:\pi\:r\:(\:r\:+\:h\:)}\\\\\implies\sf\:600\:=\:2\:\times\:\frac{22}{7}\:\times\:5\:(\:5\:+\:h\:)\\\\\implies\sf\:\dfrac{\cancel{600}\:\times\:7}{2\:\times\:22\:\times\:\cancel{5}}\:=\:5\:+\:h\\\\\implies\sf\:\dfrac{\cancel{120}\:\times\:7}{\cancel{2}\:\times\:22}\:=\:5\:+\:h\\\\\implies\sf\:\dfrac{\cancel{60}\:\times\:7}{\cancel{22}}\:=\:5\:+\:h\\\\\implies\sf\:\dfrac{30\:\times\:7}{11}\:=\:5\:+\:h\\\\\implies\sf\:\cancel{\frac{210}{11}}\:=\:5\:+\:h\\\\\implies\sf\:19.09\:=\:5\:+\:h\\\\\implies\sf\:h\:=\:19.09\:-\:5\\\\\implies\boxed{\red{\sf\:h\:=\:14.09\:cm}}$

3.

We have given that volume of cylinder i. e.

$\sf\:V_{cylinder}\:=\:924\:m^{3}$.

Also, curved surface area of cylinder i. e.

$\sf\:CSA_{cylinder}\:=\:264\:m^{2}$

We have to find, radius and height of the cylinder.

We know that,

$\pink{\sf\:V_{cylinder}\:=\:\pi\:r^{2}\:h}\\\\\implies\sf\:924\:=\:\frac{22}{7}\:\times\:r^{2}\:\times\:h\\\\\implies\sf\:r^{2}\:.\:h\:=\:\dfrac{\cancel{924}\:\times\:7}{\cancel{22}}\\\\\implies\sf\:r^{2}\:.\:h\:=\:42\:\times\:7\\\\\implies\sf\:r^{2}\:.\:h\:=\:294\:m^{3}\:\:\:-\:-\:-\:(\:1\:)$

Now, we know that,

$\sf\:CSA_{cylinder}\:=\:2\:\pi\:r\:h\\\\\implies\sf\:264\:=\:2\:\times\:\frac{22}{7}\:r\:\times\:h\\\\\implies\sf\:r.\:h\:=\:\dfrac{\cancel{264}\:\times\:7}{2\:\times\:\cancel{22}}\\\\\implies\sf\:r.\:h\:=\:\dfrac{\cancel{12}\:\times\:7}{\cancel{2}}\\\\\implies\sf\:r.\:h\:=\:6\:\times\:7\\\\\implies\sf\:r\:.\:h\:=\:42\:m^{2}\:\:\:-\:-\:-\:(\:2\:)$

Now,

$\sf\:r^{2}\:.\:h\:=\:294\:m^{3}\:\:\:-\:-\:-\:(\:1\:)\\\\\implies\sf\:r\:\times\:r\:\times\:h\:=\:294\\\\\implies\sf\:r\:\times\:42\:=\:294\:\:\:-\:-\:[\:From\:(\:2\:)\:]\\\\\implies\sf\:r\:=\:\cancel{\frac{294}{42}}\\\\\implies\boxed{\red{\sf\:r\:=\:7\:m}}$

Now, by substituting r = 7 in equation ( 2 ), we get,

$\sf\:r\:\times\:h\:=\:42\:\:\:-\:-\:-\:(\:2\:)\\\\\implies\sf\:7\:\times\:h\:=\:42\\\\\implies\sf\:h\:=\:\cancel{\frac{42}{7}}\\\\\implies\boxed{\red{\sf\:h\:=\:6\:m}}$