find the capacity of conical vessel in liters if radius is 7cm and it's slant height is 25cm
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VOLUME:
The space occupied by an object solid body is called the volume of the particular object solid body volume is always measured in cubic unit.
Volume of a liquid that can fill the interior of the hollow is called the capacity of the hollow object.
Right circular cone:
If a right angled triangle is revolved about one of the two sides forming a right angle keeping the other side fixed in position then the solid so obtained by segments is called right circular cone.
Slant height:
The length of the line segment joining the vertex to any point on a circular edge of the base is called the slant height of the cone.
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Given:
(i) Radius (r) = 7 cm
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 = 625- 49
h = √576
h = 24 cm
Volume of the cone = 1/3 πr²h
= (1/3 × 22/7 × 7 × 7 × 24)
= 1232 cm³
[1 cm³= 1/1000 L]
Capacity of the vessel = (1232/1000) L= 1.232 L
Capacity of the vessel =1.232 L
(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
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Hope this will help you....