Question

How many metal doorstops 15 cm by 10 cm by 5 cm can be cast from a spherical ball of metal of diameter 400 mm?

Answer 1

`\approx \bold{44\ or\ 45}`

Explanation:

Given

Diameter of spherical metal ball = 400 mm = 40 cm

Radius of spherical metal ball = 20 cm

Volume of a sphere is given as:

`V_(Sphere) = (4)/(3)\pi r^3`

`\Rightarrow \frac{4}3 * 3.14 * 20 ^3 = 33493.33 \ cm^3`

Dimensions of metal doorstops = 15 cm by 10 cm by 5 cm

It is of cuboid shape.

Volume of a cuboid is given as:

`V_(Cuboid) = l * b* h = 15 * 10 * 5 = 750\ cm^3`

Number of such doorsteps that can be made from the metal ball is equal to Volume of metal ball divided by volume of metal doorstep.

`(33493.33)/(750) \approx \bold{44\ or\ 45}`