Question

The volume of right circular cone is 9856 cm^3. The diameter of its base is 28 cm, find the following :
(i) height of the cone
(ii) slant height of the cone
(iii) curved surface area of the cone

Answer 1

$\huge\mathfrak{Solution:}$

Let the radius of the base of the cone be r cm

From the question, 2r = 28

Therefore, r = 14 cm

(i) Let the height of the cone be h cm

Now, volume of the cone = 1/3 × pi × r^2 × h cm^3

Therefore, 9856 = 1/3 × 22/7 × 14 × 14 × h

Therefore, h = 3 × 9856 / 22 × 2 × 14 = 48 cm

(ii) Suppose the slant height of the cone = l

Now, l^2 = h^2 + r^2

= 48^2 + 14^2

= 2304 + 196

= 2500

Therefore, l = root 2500 = 50 cm

(iii) Curved surface area of the cone = pi × r × l

= 22/7 × 14 × 50 cm^2

= 2200 cm^2

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Answer 2

$\huge\mathfrak{Solution:}$

Let the radius of the base of the cone be r cm

From the question, 2r = 28

Therefore, r = 14 cm

(i) Let the height of the cone be h cm

Now, volume of the cone = 1/3 × pi × r^2 × h cm^3

Therefore, 9856 = 1/3 × 22/7 × 14 × 14 × h

Therefore, h = 3 × 9856 / 22 × 2 × 14 = 48 cm

(ii) Suppose the slant height of the cone = l

Now, l^2 = h^2 + r^2

= 48^2 + 14^2

= 2304 + 196

= 2500

Therefore, l = root 2500 = 50 cm

(iii) Curved surface area of the cone = pi × r × l

= 22/7 × 14 × 50 cm^2

= 2200 cm^2

____________________

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