Question

Lateral surface area of a cylinder is 150 cm2 and height is 10 cm. find radiu s and volume take pi 3.14 .



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Answer 1

Step-by-step explanation:

Lateral surface area of cylinder = 150 cm² (Given)

Lateral surface area of cylinder = 2πrh

h = 10 cm

Take π =3.14

2 × 3.14 × r × 10 = 150 cm²

62.8r = 150 cm²

628r/10 = 150 cm²

628r = 150×10

r = 1500/628

r = 2.3885

Estimate 2.3885 to 2.4.

∴ r = 2.4 cm

Volume = πr²h

= 3.14 ×2.4²×10

= 180.864

Estimate 180.864 to 180.9 cm³

Hence radius = 2.4 cm and Volume = 180.9 cm³

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Answer 2

Answer:

Answer:

Radius of cylinder ≈ 2.38 cm

Volume of cylinder ≈ 177.72 cm³

Step-by-step explanation:

Given :-

Lateral surface area of cylinder = 150 cm²

Height of cylinder = 10 cm

To Find :-

Radius of cylinder and volume of cylinder?

Solution :-

Lateral surface area is also known as curved surface area (CSA). Here, using formula of CSA of cylinder to find it's radius. As we know that;

✪ CSA of cylinder = 2πrh ✪

Where,

r denotes radius of cylinder

h denotes height of cylinder

We have,

h = 10 cm

π = 3.14

CSA of cylinder = 150 cm²

Putting values in formula,

➙ 150 = 2 × 3.14 × r × 10

➙ 150 = 2 × 3.14 × 10 × r

➙ 150 = 2 × 31.4 × r

➙ 150 = 62.8 × r

➙ 150/62.8 = r

➙ 2.38 = r

➙ r ≈ 2.38 cm

Hence, radius of base of cylinder is 2.38 cm (approx).

Now, using formula of volume of cylinder to find it's volume. As we know that;

✪ Volume of cylinder = πr²h ✪

Where,

r denotes radius of cylinder

h denotes height of cylinder

We have,

r = 2.38 cm

h = 10 cm

π = 3.14

Putting all values,

➙ Volume of cylinder = 3.14 × (2.38)² × 10

➙ Volume of cylinder = 3.14 × 10 × (2.38)²

➙ Volume of cylinder = 31.4 × (2.38)²

➙ Volume of cylinder = 31.4 × 2.38 × 2.38

➙ Volume of cylinder = 31.4 × 5.66

➙ Volume of cylinder ≈ 177.72 cm³

Hence, volume of cylinder is 177.72 cm³ (approx).

Important Formulae :-

↠ TSA of cube = 6a²

↠ CSA of cube = 4a²

↠ Volume of cube = a³

↠ TSA of cuboid = 2(lb + bh + hl)

↠ CSA of cuboid = 2(l + b)h

↠ Volume of cuboid = l × b × h

↠ TSA of cylinder = 2πr(r + h)

↠ CSA of cylinder = 2πrh

↠ Volume of cylinder = πr²h

↠ Volume of hollow cylinder = πh(R²-r²)

↠ TSA of cone = πr(l + r)

↠ CSA of cone = πrl

↠ Volume of cone = 1/3πr²h

↠ SA of sphere = 4πr²

↠ Volume of sphere = 4/3πr³

↠ TSA of hemisphere = 3πr²

↠ CSA of hemisphere = 2πr²

↠ Volume of hemisphere = 2/3πr³

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