Question

Find the capacity in litres of a conical vessel with :
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm.

Answer 1

Given : Conical vessel with   (i) radius 7 cm, slant height 25 cm and  (ii) height 12 cm, slant height 13 cm.

 

(i)  Radius (r) = 7 cm and Slant height (l) = 25 cm

Let 'h' be the height of the conical vessel.

Slant height (l)² = r² + h²

h = √l² -  r²

h = √25² -  7²  

h = 625 -  49

h = √576

h = 24 cm

Height of the conical vessel = 24 cm

 

Volume of the cone ,V = 1/3 πr²h

V = (1/3 × 22/7 × 7 × 7 × 24)

V = 22 × 7 × 8

V = 1232 cm³

[1 cm³ = 1/1000 L]

Capacity of the vessel = (1232/1000) L= 1.232 L

Hence, the Capacity of the vessel is 1.232 L

 

 

(ii) Height (h) = 12 cm and Slant height (l) = 13 cm

Let 'r' be the radius of the conical vessel.

Slant height (l)²= r²+ h²

r = √ r² - h²

r = √13² -  12²

r = √169 - 144

r = √25

r = 5 cm

 

Volume of the cone,V = 1/3 πr²h

V = (1/3 × 22/7 × 5 × 5 × 12

V = 22/7 × 25 × 4

V = 22/7 × 100

V = (2200/7) cm³

Capacity of the vessel = (2200/7× 1000) L

= 11/35 l = 0.31428 L

Capacity of the vessel = 0.31428 L

Hence, the Capacity of the vessel is 0.31428 L

HOPE THIS ANSWER WILL HELP YOU…..

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Answer 2

Step-by-step explanation:

(ii) Given: Height (h) = 12 cm

Slant height (l) = 13 cm

Let r be the radius of the conical vessel.

Slant height (l)²= r²+h²

r = √ r² - h²

r = √13²– 12²

= √169 – 144

r = √25

r = 5 cm

Volume of the cone = 1/3 πr²h

= (1/3 × 22/7 × 5 × 5 × 12)

= (2200/7) cm³

Capacity of the vessel = (2200/7× 1000) L

= 11/35 L

Capacity of the vessel =11/35 L