Question

The diameter of circular base of a cylinder is 7 metres. If volume is 770cu.m.Then find its height and total surface area?​

Answer 1

Answer:

• Height of cylinder is 20 m.
• Total surface area of cylinder is 517 m².

Step-by-step explanation:

Given :-

• The Diameter of base of cylinder is 7 m.
• Volume of cylinder of 770 m³.

To find :-

• Height of cylinder.
• Total surface area of cylinder.

Solution :-

Radius = Diameter/2

$\longrightarrow$ Radius = 7/2

$\longrightarrow$ Radius = 3.5

Volume of cylinder = πr²h

Where,

• r is radius of cylinder.
• h is height of cylinder.

Put values :

$\longrightarrow$ 770 = πr²h

$\longrightarrow$ 770 = 22/7 × (3.5)² × h

$\longrightarrow$ 770 = 22/7 × 12.25 × h

$\longrightarrow$ 770 × 7 = 269.5 × h

$\longrightarrow$ 5390 = 269.5 × h

$\longrightarrow$ 5390/269.5 × h

$\longrightarrow$ h = 20

Thus,

Height of cylinder is 20 m.

Now,

We know,

Total surface area of cylinder = 2πr² + 2πrh

$\longrightarrow$ 2 × 22/7 × (3.5)² + 2 × 22/7 × 3.5 × 20

$\longrightarrow$ 44/7 × 12.25 + 44/7 × 70

$\longrightarrow$ 539/7 + 3080/7

$\longrightarrow$ 77 + 440

$\longrightarrow$ 517

Therefore,

Total surface area of cylinder is 517 m².

Answer 2

Answer:

$\huge\underline\mathfrak\red{question}$

The diameter of circular bade of cylinder is 7 meters. If volume is 77cubic meters. Then find its height and total surface area?

$\huge\underline\bold{understanding\:the\: question}}}}</p><p></p><p>in the question it's saying that we have to find height of the cylinder and total surface area of cylinder.</p><p>so first step we have to find height then we we have to find total surface area of cylinder.</p><p></p><p>[tex]\huge\underline\mathfrak\blue{Answer}$

let's find out:-

• diameter is given:- 7 m
• and the volume is:- 770m

=> first find radius:-

$radius = \frac{d}{2}$

$radius = \frac{7}{2}$

$radius = 3.5$

=> now, find the height of the cylinder

use formula:-

$volume \: of \: cylinder \: \\ = \pi {r}^{2} h$

now find the height:-

$770 = \frac{22}{7} \times 3.5 \times 3.5 \times h$

$770 = \frac{22}{1} \times 0.5 \times 3.5 \times h$

$770 = 38.50 \times h$

$\frac{770}{38.5} = h$

$20 = h$

hence, height=20m

according to the question:-

now we have to find surface area of cylinder:-

:- use formula:-

$surface \: area \: of \: cylinder = \\ 2\pi \: r(r + h)$

$2 \times \frac{22}{7} \times 3.5(3.5 + 20)$

$= 2 \times 22 \times 0.5(23.5)$

$= 66 \times 23.5$

$= 1551 {m}^{2}$

hence we find height=20 m²

and surface area of cylinder=1551m²