How many spherical lead shot is having diameter 3 cm can be made from a cuboidal solid of dimensions 9cm*11cm*12 cm?
Answers
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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