Question

A cuboidal block of metal measuring 45cm * 30cm*0.5m was melted and recast into cubical blocks each with an edge of length 3 cm.
(i) Find the number of cubes that can be made.
(ii) What is the cost of polishing the surface of the cubes at the rate of ₹1.25 per cm²?​

Answer 1

(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]

= $\frac{67500}{27}$

= 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

------------------------------------------------------------------------------------------

Also View:

A CUBE AND A CUBOID HAVE THE SAME VOLUME.THE DIMENSIONS OF THE CUBOID ARE IN THE RATIO 1:2:4.IF THE DIFFERENCE BETWEEN THE COST OF POLISHING THE CUBOID AND THE CUBE AT THE RATE OF RS.5 PER SQUARE METER IS RS.8O.FIND THEIR VOLUMES.

https://brainly.in/question/526568

The volume of a cubical solid is 10368 cm cube if its dimensions are in the ratio 3 : 2 : 1 find the find the cost of polishing its total surface @ rupees 2.5 per metre square .

https://brainly.in/question/2411453

Find the cost of polishing a cuboid at Rs.2.50 per sq.m whose length, breadth and height are 4m,3.5m,and 3m respectively .

https://brainly.in/question/8830911

Answer 2

Answer:

(I) 2500 blocks

(ll) 168750 rs

Step-by-step explanation:

Volume of cuboid is L*B*H= 45x30x50= 67500cm^3

Volume of each cubical block= 3x3x3= 27cm^3

Number of blocks we get are= 67500/27= 2500 blocks

Surface area of cube= 6x(side)^2= 6x3^2= 54.

Total surface area of 2500 cubical blocks:

2500x54= 135000cm^2

Cost of polishing is rs 1.25

So polishing cost= 135000x1.25= 168750 rs