Question

The diameter of a circular base of a cylinder is 7 if volume is 770 cu.mm then find its height and total surface area

Answer 1

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

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

⟶ Radius = 7/2

⟶ Radius = 3.5

☆Volume of cylinder = πr²h

⇩Where,

☘r is radius of cylinder.

☘h is height of cylinder.

◇Put values :

⟶ 770 = πr²h

⟶ 770 = 22/7 × (3.5)² × h

⟶ 770 = 22/7 × 12.25 × h

⟶770 × 7 = 269.5 × h

⟶ 5390 = 269.5 × h

⟶ 5390/269.5 × h

⟶ h = 20

Thus,⇣

Height of cylinder is 20 m.

Now,⇣

We know,

Total surface area of cylinder = 2πr² + 2πrh

⟶ 2 × 22/7 × (3.5)² + 2 × 22/7 × 3.5 × 20

⟶ 44/7 × 12.25 + 44/7 × 70

⟶ 539/7 + 3080/7

⟶ 77 + 440

⟶ 517

Therefore,⟱

◆Total surface area of cylinder is 517 m².

Answer 2

Answer:

Height of cylinder is 20 m.

Total surface area of cylinder is 517 m².

Step-by-step explanation:

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

✯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

⟶ Radius = 7/2

⟶ Radius = 3.5

☆Volume of cylinder = πr²h

⇩Where,

☘r is radius of cylinder.

☘h is height of cylinder.

◇Put values :

⟶ 770 = πr²h

⟶ 770 = 22/7 × (3.5)² × h

⟶ 770 = 22/7 × 12.25 × h

⟶770 × 7 = 269.5 × h

⟶ 5390 = 269.5 × h

⟶ 5390/269.5 × h

⟶ h = 20

Thus,⇣

Height of cylinder is 20 m.

Now,⇣

We know,

Total surface area of cylinder = 2πr² + 2πrh

⟶ 2 × 22/7 × (3.5)² + 2 × 22/7 × 3.5 × 20

⟶ 44/7 × 12.25 + 44/7 × 70

⟶ 539/7 + 3080/7

⟶ 77 + 440

⟶ 517

Therefore,⟱

◆Total surface area of cylinder is 517 m².