Question

6.
The height of a cone is 3m and the diameter of its base is 8m. Find its
1) Slant height.
ii) curved surface area ( C.S.A).
Total surface area ( T.S.A).
iv)
Volume.​

Answer 1

GivEn:

• Height of cone, h = 3 m
• Diameter of cone, d = 8 m
• Radius of cone, r = 8/2 = 4 m

To find:

• Slant height
• Curved surface area
• Total surface area
• Volume of cone

Solution:

i) Slant height of cone

☯ Let slant height of cone be l cm.

We know that,

Slant height = √(radius)² + (height)²

⇒ l = √r² + h²

⇒ l = √4² + 3²

⇒ l = √16 + 9

⇒ l = √25

⇒ l = 5 m

Thus, Slant height of cone is 5 m.

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ii) Curved surface area of cone

As we know that,

CSA of cone = πrl

Here,

• r = 4 m
• l = 5 m

Putting values,

⇒ 22/7 × 4 × 5

⇒ 62.857 m².

Thus, CSA of cone is 62.857 m²

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iii) Total surface area of cone

As we know that,

TSA of cone = πr(r + l)

⇒ 22/7 × 4(4 + 5)

⇒ 22/7 × 4 × 9

⇒ 113.142 m² (approx)

Thus, TSA of cone is 113.142 m².

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iv) Volume of cone

As we know that,

Volume of cone = 1/3 πr²h

Here,

• r = 4 m
• h = 3 m

Therefore,

⇒ 1/3 × 22/7 × 4² × 3

⇒ 1/3 × 22/7 × 16 × 3

⇒ 22/7 × 16

⇒ 50.285 m³ (approx)

Hence, Volume of cone is 50.285 m³.