Question

C. The diameter of the base of a right circular cone is 10m and its slant height is 13 cm
height is 13cm. Calculate:
i) Height of the cone.
ii) Curved surface area of the cone.
Total surface area of the cone.
iv) The volume of the cone. (1= 3.14)​

Answer 1

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Given :-

• The diameter of the base of a right circular cone is 10cm.

• Its slant height is 13 cm.

To Find :-

• The Height of the cone.

• The curved surface area of the cone.

• Total surface area of the cone.

• The volume of the cone.

Hint Given :-

( π = 3.14)

Know About it :-

A cone where the its axis is the line meeting the vertex to the midpoint of the circular base whose centre point is joined with the vertex to the base of the cone making a right angle.

h = hieght of cone

r = radius of base

l = slant hieght

Solution :-

Case 1 :-

★ Height of the cone

Using , l = √( r² +h² )

We have,

• l = 13 cm

➝ diameter = 10 cm , r = 10/2 ,

• r = 5 cm

l = √( r² +h² )

➝ l² = r² + h²

➝ h² = l² - r²

➝ h² = 13² - 5²

➝ h² = 169 - 25

➝ h² = 144

➝ h = √ 144

➝ h = 12 cm.

So, Hieght of cone is 12 cm.

Case 2 :-

★ Curved surface area of the cone = π r l

= 3.14 × 5 × 12

= 188.4 cm²

So, Curved surface area of the cone is 188.4 cm² .

Case 3 :-

★ Total surface area of the cone = π(r + l) r

= 3.14 × ( 5+ 13 ) 5

= 3.14 × 18 × 5

= 282.6 cm²

So, Total surface area of the cone is 282.6 cm².

Case 4 :-

★ The volume of the cone = 1/3π r² h

= 1/3 × 3.14 × 5 × 5 × 14

= 1/3 × 3.14 × 25 × 14

= 366.4 cm³

So, The volume of the cone is 366.4 cm³.

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