Question

Total surface area of a cylinder is 7480 square cm and its radius is 14 cm.find its height and volume?​

Answer 1

Answer:

given r = 14cm

volume = πr^h

Step-by-step explanation:

now,

7480= πr^2h

=22/7 × 14 × 14

= 22 × 14× 7

= 2086 × h

h = 2086/ 7480

h = 3.59 cm....

Answer 2

Given :

• Total Surface Area is 7480 Square Cente metre
• Radius of the cylinder is 14 cm

To Find :

• Height of the cylinder
• Volume of the cylinder

Explanation :

• it's have been asked to find the height and volume of the cylinder. We have to find the height of the cylinder first by substituting the values in the formula of Total Surface Area of the cylinder as given below :

$\underline{\boxed{\sf Total\:Surface\:Area_{(Cylinder)}=2\pi r(h+r)\:cm^2}}$

• The volume of cylinder can be found by using the formula of Volume of Cylinder as given below :

$\underline{\boxed{\sf Volume _{(Cylinder)}=\pi r^2h \: cm^3 }}$

Solution :

(i) Height of the cylinder

$\sf Total\:Surface\:Area\:Of\:Cylinder=2\pi r(h+r)\:cm^2$

$\sf \rightarrow 7480 = \dfrac{22}{\cancel{7}}\times {\cancel{14}}\times (h+14)$

$\sf \rightarrow 7480 = 22\times 2 \times (h+14)$

$\sf \rightarrow 7480 = 88 \times (h+14)$

$\sf \rightarrow 7480 = 88h + 1232$

$\sf \rightarrow 7480 - 1232 = 88h$

$\sf \rightarrow 6248 = 88h$

$\sf \rightarrow \dfrac{6248}{88} = h$

$\sf \rightarrow h = 71 \: cm$

(ii) Volume of the cylinder

$\sf Volume \:Of\: Cylinder = \pi r^2h \:cm^3$

$\sf \rightarrow \dfrac{22}{\cancel{7}} \times 14 \times 14 \times 71$

$\sf \rightarrow 22 \times 2 \times 14 \times 71$

$\sf \rightarrow 308 \times 142$

$\sf \rightarrow 43,736\: cm^3$

________________________________

Required Answer :

Height of the cylinder is $\underline{\sf 71 \: cm}$

Volume of Cylinder is $\sf \underline{\sf 43,736\: cm^3}$

________________________________