how many spherical lead shots each having diameter 3cm can be made from a cuboidal lead solid of dimensions 9cm*11cm*12cm.
Answers
Radius of spherical lead shots = 3/2 = 1.5 cm
Volume of 1 spherical lead shot = (4/3)*pi*(r^3) ------(1)
Volume of Cuboid = l*b*h = 9*11*12 ---------(2)
Hence number of spherical shots required = Volume of Cuboid / Volume of 1 spherical lead shot.
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Thanks,
Midhun
Given that
The dimensions of a cuboidal lead solid =
= 9 cm × 11 cm × 12 cm
We need to find the number of spherical lead shots, each of diameter 3 cm that can be made from the cuboidal solid.
According to the given information, the length, the breadth and the height of the cuboidal lead solid are,
L = 9 cm, B = 11 cm, H = 9 cm
Let the required number of spherical lead shots be x.
The lead shot is spherical in shape.
Thus, volume of a lead shot = 4/3πr^3
As the diameter of each lead shot is 3 cm,
⇒Radius of a spherical lead shot =
= 1/2 x diameter
= 1/2 x 3
= 3/2
⇒Volume of the cuboidal lead solid = L x B x H
= 9 cm x 11 cm x 12cm
Volume of the spherical lead shot =
= (4/3) × (22/7) × (3/2)^3
Therefore the number of spherical lead shots x
= (9 x 11 x 12) / [(4/3) × (22/7) × (3/2)^3]
= 84
Thus, the required number of spherical lead shots is 84.
Explanation:
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