The given fi gure shows two cubes made of the same material. One cube has sides that arc thrice as long as the other cube. The weight of the small cube is 10 N.

What is the weight of the larger cube?

Options

A. 30 N
B. 80 N
C. 120 N
D. 270 N

Answer

D

Explanation

Since, the two cubes are made of the same material, so, let the density of both cubes be p.
Length of smaller cube = x
`therefore` Volume of smaller cube, `V_1 = x^3`
Mass of smaller cube, `m_1 = V_1p = x^3p`
Weight of smaller cube, `W_1 = m_1g = x^3pg `
but `W_1`=10 N
`thereforex^3pg=10N`
Length of larger cube = 3x
`therefore` Volume of larger cube, `V_2=(3x)^3=27x^3`
Mass of larger cube, `m_2=V_2p=27x^3p`
Weight of larger cube, `W_2=m_2g=27x^3pg`
`=27xx10N=270N`