Question

A cube of a metal of 5 cm edge is melted and casted into a cuboid whose base is 2·50 cm × 0·50 cm. Find the height of the cuboid.
Also find the surface areas of cube and cuboid.

Answer 1

Height of cuboid = 100 cm

TSA of cube = 150 sq. cm

TSA of cuboid = 602.5 sq.cm

Explanation:

Given: A cube of a metal of 5 cm edge is melted and casted into a cuboid whose base is 2·50 cm × 0·50 cm.  

Volume of cube = volume of cuboid

a * a * a = l * b * h

5 * 5 * 5 = 2.5 * 0.5 * h

h = 5 * 5 * 5 / (2.5 * 0.5)

h = 100 cm

Surface area of cube = 6a*a = 6 * 5 * 5 = 150 sq. cm.

Surface area of cuboid =  2 (lb + bh + lh) = 2 (2.5*0.5 + 0.5*100 + 100*2.5)

=  2 (1.25 + 50 + 250)

= 2* 301.25

= 602.5 sq.cm

Answer 2

Required answer:-

Question :

• A cube of a metal of 5 cm edge is melted and casted into a cuboid whose base is 2·50 cm × 0·50 cm. Find the height of the cuboid.

Also, find the surface areas of cube and cuboid.

Solution :

Given that,

Base of cuboid after casted = 2.50 cm × 0.50 cm

Size of edge of cube of a metal = 5 cm

Formulaes used :

♦ Total surface area for cube = 6a²

♦ Total surface area for cuboid = 2 (l.b + b.h + h.l)

Step by step explaination –

$Volume \: of \: cuboid \: = volume \: of \: melted \: cube \\ 2.50 \: × 0.50 \: × height \: = (5)³ \\ h \: = \: \frac{5 \times 5 \times 5}{2.50 \times 0.50} cm \\ = 100 \: cm \: \\ Thus \: height \: of \: cuboid \: is \: 100 \: cm$

Now, we have to calculate the total surface area of cube.

Total surface area of cube = 6a²

= 6(5)² cm²

= 150 cm²

Now, we have to calculate the total surface area of cuboid.

Total surface area of cuboid = 2(l×b + b×h + h×l)

= 2 (2.50×0.50 + 0.50×100 + 100×2.50) cm²

= 602.50 cm²

Answer :

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Height of cuboid = 100 cm

Surface area of cube = 150 cm²

Surface area of cuboid = 602.50 cm²

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