Question

The total surface area of cylinder is 8448 sq cm if radius of its base is 28 cm what is its height ​

Answer 1

$\bf \: \underline{ Given }\: :$ ↴

$\sf \: Total \: surface \: area \: of \: cylinder = 8448 \: cm ^{2}$

$\sf \: Radius \: of \: it's \: base = 28 \: cm$

$\bf \: \underline{ To \: find} \: :$ ↴

$\sf \: We \: have \: to \: find \: the \: height \: of \: the \: cylinder.$

$\bf \: \star \: { \underline{So, \: Let's \: Start}} \: \star$

$\sf \: We \: know \: that \: :$ ↴

$\boxed{ \red{\sf \: Total \: surface \: area \: of \: cylinder \: = \: 2\pi\:r \: (Height + Radius)}}$

$\sf \underline{Putting \: the \: values} :$ ↴

$\sf \: \implies \: 8448 = 2 \: \times \: \dfrac{22}{7} \: \times 28 \: (height + 28 )$

$\sf \:\implies \: \dfrac{8448 \times 7}{ 2 \times 22} \: \times 28 \: (height + 28 )$

$\sf \:\implies \: 1344 \: = \: 28 \: (height+28)$

$\sf \: \implies \: \dfrac{1344}{28} \: = \: height+28$

$\sf \:\implies \: 48 \: = \: height+28$

$\red{ \sf \: \implies \: Height = 20}$

$\purple{ \sf \: Thus, \: height \: of \: the \: cylinder \: is \: 20 \: cm. }$

Answer 2

Given :

• TSA of cylinder = 8448cm²

• Radius of base = 28cm

To Find :

• Height Of cylinder

Solution :

✬ Here in the question Total surface area of cylinder is given that is 8448cm² and radius of its base is 28cm and We have to find the height. As we know that Total surface area of cylinder is 2πr (h + r), by Putting values in the formula we can easily find the Height of the cylinder.

TSA of cylinder = 2πr (H + r)

⇝ 8448 = 2 × 22/7 × 28 (H + 28)

⇝ 8448 = 44 × 4(H + 28)

⇝ 8448 = 176 (H + 28)

⇝ 8448/176 = H + 28

⇝ 48 = H + 28

⇝ H = 48 - 28

⇝ Height = 20cm

_________________

Verification :

TSA of cylinder = 2πr (H + r)

⇝ 8448 = 2 × 22/7 × 28 (28 + 20)

⇝ 8448 = 176 × 48

⇝ 8448 = 8448

Hence, Proved

_________________

∴ Height of cylinder is 20cm