Question

The volume and CSA of a cylinder is 2310 cm and 660 cm respectively find its base radius and height.​

Answer 1

Step-by-step explanation:

Given:-

• The volume of the cylinder = 2310 cm³.

• The CSA of cylinder = 660cm²

To Find:-

• The base radius and height of the cylinder.

Solution:-

Let the radius of the cylinder be " r " and height be " h "

CSA of cylinder = 2πrh

$\sf \implies2\pi rh = 660$

$\sf \implies2 \times \dfrac{22}{7} \times ( r\times h) = 660$

$\sf \implies r\times h = 660 \times \dfrac{7}{22 \times 2}$

$\sf \implies r\times h = 105....(i)$

The volume of the cylinder = 2310

$\sf \implies \pi {r}^{2}h = 2310$

$\sf \implies \dfrac{22}{7}\times {r}^{2}h = 2310$

$\sf \implies r \times (r \times h) = 2310 \times \dfrac{7}{22}$

$\sf \implies r \times 105= 735 \: \: \:\:\: \big[From\: equation\: (i)\big]$

$\sf \implies r = \dfrac{735}{105}$

$\sf \implies r = 7$

Substitute r = 7 in equation (i)

$\sf \implies r\times h = 105$

$\sf \implies 7\times h = 105$

$\sf \implies h = \dfrac{105}{7}$

$\sf \implies h = 15$

Therefore:-

Base radius of the cylinder = 7cm

Height of the cylinder = 15cm

Answer 2

Solution

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Given,

• the volume of the cylinder = 2310cm^3
• the curved surface area of cylinder = 660cm^2 .

To find ,

• the base radius and height of the cylinder .

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

So,

In case 1

• CSA of the cylinder = 2πrh

=> 660 = 2πrh

=> 660 = 2×22/7×(r×h)

=> r×h = 660×7/22×2

=> r ×h = 105

Now,

• the volume of the cylinder is 2310 cm^3

So,

πr^2 h = 2310

=> 22/7 × r^2 h =2310

=> r^2 × h = 2310 × 7/22

=> r(r×h) = 2310 × 7/22

=> r × 105 = 735 [ from the case1 ]

=> r = 735 / 105

=> r = 7

• now Putting r= 7 in the case 1 we get ;

=> r × h = 105

=> 7 × h = 105

=> h = 105/7

=> h = 15

The radius is 7cm and the height of the cylinder is 15 .

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