Question

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 is 3 m .

⬤ Diameter of its Base is 8 m .

To Find :

⬤ Slant Height .

⬤ Curved Surface Area .

⬤ Total Surface Area .

⬤ Volume .

Solution :

• Diameter = 8
• Radius = 8/2 = 4 m.

1) Slant Height .

Formula Used :

$\sf[\:{Slant\:Height=l=\sqrt{{h}^{2}+{r}^{2}}\:]}$

Now :

l = √h² + r²

l = √(3)² + (4)²

l = √(3×3) + (4×4)

l = √9 + 16

l = √25

l = 5

Therefore , The Slant Height of the Cone is 5 m .

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2) Curved Surface Area .

Formula Used :

$\sf[\:{Curved\:Surface\:Area\:of\:Cone=\pi{r}l}\:]$

Now :

πrl

22/7 × 4 × 5

440/7

62.85

Therefore , The Curved Surface Area of Cone is 62.85 m² .

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3) Total Surface Area .

Formula Used :

$\sf[\:{Total\:Surface\:Area\:of\:Cone=\pi{r}(l+r)}\:]$

Now :

πr (l + r)

22/7 × 4 (5 + 4)

88/7 × 9

792/7

113.14

Therefore , The Total Surface Area of Cone is 123.24 m² .

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4) Volume .

Formula Used :

$\sf[\:{Volume\: of\:Cone=\dfrac{1}{3}\pi{r}^{2}h}\:]$

Now :

1/3πr²h

1/3 × 22/7 × 4 × 4 × 3

22/7 × 4 × 4

372/7

50.28

Therefore , The Volume of the Cone is 50.38 m² .