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प्रश्न
The dimensions of a cuboid are 44 cm, 21 cm, 12 cm. It is melted and a cone of height 24 cm is made. Find the radius of its base.
उत्तर
The dimensions of the cuboid are 44 cm, 21 cm and 12 cm.
Let the radius of the cone be r cm.
Height of the cone, h = 24 cm
It is given that cuboid is melted to form a cone.
∴ Volume of metal in cone = Volume of metal in cuboid
= `1/3pir^2h = 44 xx 21 xx 12` (Volume of cuboid = Length × Breadth × Height)
\[ \Rightarrow \frac{1}{3} \times \frac{22}{7} \times r^2 \times 24 = 44 \times 21 \times 12\]
\[ \Rightarrow r = \sqrt{\frac{44 \times 21 \times 12 \times 21}{22 \times 24}} = \sqrt{21 \times 21} = 21 cm\]
Thus, the radius of the base of cone is 21 cm.
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