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प्रश्न
A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.
उत्तर
(i) Whenever we placed a solid right circular cone in a right circular cylinder with full of water,
Then volume of a solid right circular cone is equal to the volume of water failed from the cylinder.
(ii) Total volume of water in a cylinder is equal to the volume of the cylinder.
(iii) Volume of water left in the cylinder = Volume of the right circular cylinder – volume of a right circular cone.
Now, given that
Height of a right circular cone = 120 cm
Radius of a right circular cone = 60 cm
∴ Volume of a right circular cone
= `1/3 pir^2 xx h`
= `1/3 xx 22/7 xx 60 xx 60 xx 120`
= `22/7 xx 20 xx 60 xx 120`
= 144000π cm3
∴ Volume of a right circular cone
= Volume of water falled from the cylinder
= 144000π cm3 ...[From point (i)]
Given that, height of a right circular cylinder = 180 cm
And radius of a right circular cylinder
= Radius of a right circular cone
= 60 cm
∴ Volume of a right circular cylinder
= πr2 × h
= π × 60 × 60 × 180
= 648000π cm3
So, volume of a right circular cylinder
= Total volume of water in a cylinder
= 648000π cm3 ...[From point (ii)]
From point (iii),
Volume of water left in the cylinder
= Total volume of water in a cylinder – Volume of water falled from the cylinder when sold cone is placed in it
= 648000π – 144000π
= 504000π
= `504000 xx 22/7`
= 1584000 cm3
= `1584000/(10)^6 m^3`
= 1.584 m3
Hence, the required volume of water left in the cylinder is 1.584 m3.
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