Question

the surface area of a sphereif is 154² cm find the volume​

Answer 1

Answer:

Step-by-step explanation:

GIVEN :

Surface area of sphere = 154 cm²

Surface area of sphere = 4πr²

154 = 4 ×(22/7) × r²

154 × 7 = 88r²

r² = (154×7) /88

r² = (7 × 7 )/4

r² = 49 /4

r = √49/4 = 7/2

r = 7/2 cm

Volume of Sphere = 4/3 πr³

=( 4/3) × (22/7) × (7/2)³

= 4/3 × 22/7 × (7/2) × (7/2) × (7/2)

= (22 × 7 × 7) /(3×2)

=( 22 × 49) / 6= 1078/6 = 179.66 cm³

Volume of Sphere = 179.66 cm³

Hence, the Volume of Sphere is 179.66 cm³.

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Answer 2

Given :

• Surface area of sphere = 154 cm²

To find :

• Volume of the sphere

Concept Used :

→ Formula of surface area of sphere :-

• Surface area of sphere = 4πr²

→ Formula of volume of sphere :-

• Volume of sphere = 4/3 πr³

where,

• Take π = 22/7
• r = radius of the sphere

Firstly, by using the formula of surface area of sphere, we will find the value of the radius of the sphere then by substituting the values in the formula of volume of sphere we will get our required answer.

Solution :

Using formula,

→ Surface area of sphere = 4πr²

Substituting the given values,

⇒ 154 = 4πr²

⇒ 154 = 4 × 22/7 × r²

⇒ 154 = 88/7 × r²

⇒ 154 × 7/88 = r²

⇒ 77 × 7/44 = r²

⇒ 7 × 7/4 = r²

⇒ 49/4 = r²

⇒ Taking square root on both the sides.

⇒ √49/4 = r

⇒ ± 7/2 Reject -ve = r

⇒ 7/2 = r

The value of r = 7/2 cm

• Radius of sphere = 7/2 cm

Using formula,

→ Volume of sphere = 4/3 πr³

⇒ Volume = 4/3 × 22/7 × (7/2)³

⇒ Volume = 4/3 × 22/7 × 7/2 × 7/2 × 7/2

⇒ Volume = 4/3 × 22 × 1/2 × 7/2 × 7/2

⇒ Volume = 179.67

Volume of sphere = 179.67 cm³

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Know MorE :

• Volume of cylinder = πr²h
• Volume of cone = 1/3 πr²h
• Curved surface area of cone = πrl
• Total surface area of cone = πrl + πr²h
• Total surface area of cylinder = 2πrh + 2πr²
• Area of circle = πr²
• Circumference = 2πr
• Diameter = 2 × Radius
• Radius = Diameter/2