Question

32. व्यास 21cm वाले गोले का पृष्ठीय क्षेत्रफल ज्ञात कीजिए।
Find the surface area of a sphere whose diameter is 21 cm.​

Answer 1

Answer :

• Surface area of sphere is 1386cm²

Given :

• Diameter is 21cm

To find :

• Surface area of a sphere

Solution :

Given that, Diameter is 21cm so ,

Now we have to find the radius of sphere,

As we know that,

• Radius = Diameter/2

》 Radius of sphere = 21/2 = 10.5cm

Radius of sphere is 10.5cm

Now we have to find the surface area of sphere,

As we know that,

• Surface area of sphere = 4πr²

Where,r is radius 10.5cm

》Surface area of sphere = 4πr²

》4 × 22/7 × 10.5 × 10.5

》1386cm²

Hence, Surface area of sphere is 1386cm²

Answer 2

Given :

• Shape = Sphere
• Diameter of Sphere = 21cm

To Find :

• Surface Area of Sphere

Solution :

❏ As we know that, Surface Area of Sphere is given by 4πr² . In this question diameter is given and we know that Diameter = 2 × radius . So Firstly we will find the Radius of Sphere then we will find the Surface Area of Sphere.

⠀

⟾ Radius of Sphere :

• Diameter = 2 × Radius
• 21 = 2 × Radius
• 21 / 2 = Radius
• 10.5cm = Radius

⠀

⟾ Surface Area of Sphere :

• T.S.A of Sphere = 4πr²
• T.S.A = 4 × 22/7 × (10.5)²
• T.S.A = 4 × 22/7 × 10.5 × 10.5
• T.S.A = 4 × 22/7 × 110.25
• T.S.A = 4 × 22 × 15.75
• T.S.A = 4 × 346.5
• T.S.A = 1386cm²

Thus Surface Area of Sphere is 1386cm²

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★ Additional Info :

• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πrh + 2πr²
• Volume of cone = ⅓ πr²h
• C.S.A of cone = πrl
• T.S.A of cone = πrl + πr²
• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³
• Volume of sphere = 4/3πr³
• Surface area of sphere = 4πr²
• Volume of hemisphere = ⅔ πr³
• C.S.A of hemisphere = 2πr²
• T.S.A of hemisphere = 3πr²

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