Question

The dimensions of a solid metallic cuboid are 50cm x 45cm x 30cm. It is melted and recast into
identical solid metal cubes with each of edge 5cm . Find
a) surface area of the cuboid
b) number of cubes formed
c) Find the cost of polishing the surfaces of all cubes formed at the rate of Rs110/sqm.​

Answer 1

Answer:

a) surface area of the cube is 10,200cm²

b) Number of cubes formed is 540

c) Total cost of polishing the surfaces of cube is ₹891

Step-by-step explanation:

Given dimensions if the solid metallic cube :

• l (length) = 50cm.
• b (breadth) = 45cm.
• h (height) = 30cm.

Solutions :

a) surface area of the cuboid :

→ Surface area of a cuboid is given by :

→ 2(lb + bh + lh)

From the given dimensions :

→ 2(50•45 + 45•30 + 30•50)

→ 2(2250 + 1350 + 1500)

→ 2(5100)

→ 10,200cm²

∴ The surface area of the cuboid is 10,200cm² ✔

_____________________

b) number of cubes can be formed :

Finding the volume of the cuboid :

Volume of a cuboid is given by : l • b • h

→ 50 • 45 • 30

• Here, as the cuboid recasts and forms cubes of 5cm. Therefore to find the number of cubes can be formed by the cuboid, we need to divide their volumes.

Finding the volume of the cube :

Volume of a cube : (side)³

• Each side of the cube will be taken as 5cm.

→ Volume of the cube : ( 5cm )³

→ 5 • 5 • 5cm³

Numbers of cube can be formed :

→ Volume of the cuboid/Volume of the cube.

• Volume of the cuboid = 50 • 45 • 30 cm³
• Volume of the cube = 5 • 5 • 5 cm³

Number of cubes forms :

→ 50*45*30/5*5*5

→ 10*9*6

→ 540 cubes

∴ 540 cubes can be formed.

____________________

c) Find the cost of polishing the surfaces of the cube formed, at the rate of ₹100 per m²

Finding the surface area of the cube :

Surface area of a cube is given by : ( 6a² )

• "a" represents each side of the cube.

→ Surface area of the cube : 6 • (5)²

→ 6 • 25

→ 150cm²

• We need to find the cost of polishing of 540 such cubes.

→ Surface area of 540 such cubes :

→ 540 • surface area of one cube.

• Surface area of one cube is 150cm²

So,

→ 540 • 150

→ 81,000cm²

∴ The surface area of 540 such cubes is 81,000cm²

Finding the total cost for polishing the cubes :

• rate is ₹110 per metre²

Convert the surface area in metres :

[ ∵ 1m² = 10000cm]

→ 81,000cm² = 8.10m²

So,

Cost of polishing :

→ 8.10 • 110

→ ₹891

____________________

Answer 2

Answer:

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