Question

The internal diameter of a spherical bowl half full is 20cm. The contents are poured into an empty cylindrical bottle with an internal diameter of 10cm. Calculate, correct to one decimal place, the depth of water in the bottle.

A) 5.2 cm

B) 7.6 cm

C) 10.0 cm

Answer 1

To calculate the depth of water in the cylindrical bottle, we need to determine the volume of water in the spherical bowl and then use that volume to find the depth in the cylindrical bottle.

Substituting the values we have, the height of water in the bottle is approximately 7.6 cm.

Step-by-step explanation:

To calculate the depth of water in the cylindrical bottle, we need to determine the volume of water in the spherical bowl and then use that volume to find the depth in the cylindrical bottle.

First, we need to find the radius of the spherical bowl. The internal diameter is given as 20 cm, so the radius is half of that, which is 10 cm.

Using the formula for the volume of a sphere, V = 4/3 πr³, we can calculate the volume of water in the spherical bowl. Half full means half the volume, so it will be 1/2 times the volume of the full sphere.

Next, we need to find the radius of the cylindrical bottle. The internal diameter is given as 10 cm, so the radius is half of that, which is 5 cm.

Using the formula for the volume of a cylinder, V = πr²h, we can calculate the height (depth) of water in the cylindrical bottle by rearranging the formula to solve for h: h = V / (πr²).

Substituting the values we have, the height of water in the bottle is approximately 7.6 cm.