A cuboidal block of metal measuring 45 cm x 30 cm x 0.5 m was melted and recast into cubical
each with an edge of length 3 cm.
(1 ) Find the number of cubes that can be made.
(2) What is the cost of polishing the surfaces of the cubes at the rate of 3 1.25 per cm??
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Answers
Answer:
(i) The number of cubes that can be made is 2500.
(ii) The cost of polishing the surface of the cubes at the rate of ₹1.25 per cm² is Rs. 168750.
Step-by-step explanation:
Case 1: Finding the no. of cubes that can be made
Dimensions of the cuboidal block:
Length, l = 45 cm
Breadth, b = 30 cm
Height, h = 0.5 m = 50 cm
∴ The volume of the cuboidal block = l * b * h = 45 * 30 * 50 = 67500 cm³
Dimension of each cubical blocks:
Length of the edge, a = 3 cm
∴ The volume of each cubical blocks = a³ = 3³ = 27 cm³
Thus,
The no. of cubes that can be made is given by,
= [volume of the cuboidal block] / [volume of each cubical blocks]
=
= 2500
Case 2: Finding the cost of polishing the surface of the cubes
We know that for polishing the surface of the cube we have to find the total surface area of the cube, so,
The total surface area of 1 cube = 6 * a² = 6 * 3² = 54 cm²
∴ The total surface area of 2500 cubes = 54 cm² * 2500 = 135000 cm²
The cost of polishing per cm² of the surface is = Rs. 1.25
Thus,
The cost of polishing the surface of all the cubes is,
= 135000 cm² * Rs. 1.25
= Rs. 168750
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