Question

A metal cuboid has a volume of 1080 cm3
and a mass of 8 kg. The cuboid is melted down and made into a sphere with radius r cm.
(i) Calculate the value of r.
[The volume, V, of a sphere with radius r is V =
3/4πr3.]

Answer 1

Answer:

Given a solid metal cuboid with dimension 72cm×30cm×75cm. It is melted, recast into cube of edge 6 cm.

For forming cube by melting, we have to find volume of cuboid =l×b×h

=72cm×30cm×75cm

=162000cm

3

Volume of the cube to be formed =(side)

3

=6

3

=216cm

3

So, number of cubes formed =

Volume of cube

Volume of cuboid

=

216

162000

=750

For polishing the cube we need to find total surface area of cube.

Total surface area of one cube =6×(side)

2

=6×6

2

=216cm

2

Total surface area of the 750 cubes =216cm

2

×750

=162000cm

2

=16.2m

2

Cost of polishing per sq.m is Rs. 150.

Therefore, cost of polishing 16.2 sq m =16.2m

2

×150

=Rs.2430