Question

The answer is 51.0 ml but can someone explain why please

Answer 1

`\boxed{\sf A. \ 51 \ mL}`

Step-by-step explanation:

Amount of water displaced by the sphere will be equal to the volume of complete sphere.

As the sphere completely sinks to the bottom of the cup.

We have been given;

Diameter of sphere (d) = 4.6 cm

So,

`\sf Radius \: of \: sphere \: (r) = (Diameter \: of \: sphere \: (d))/(2) \\ \sf = (4.6)/(2) \\ \sf = 2.3 \: cm`

Volume of sphere (V):

`\boxed{ \bold{V = (4)/(3) \pi {r}^(3) }}`

By substituting value of r we get:

`\sf \implies V = (4)/(3) * \pi * {(2.3)}^(3) \\ \\ \sf \implies V = (4)/(3) * 3.14 * 12.167 \\ \\ \sf \implies V = (152.81752)/(3) \\ \\ \sf \implies V = 50.94 \: {cm}^(3) \\ \\ \sf \implies V \approx 51 \: {cm}^( 3)`

1 cm³ = 1 mL

`\therefore`

V = 51 mL

So,

Water displaced by the sphere = 51 mL