# Lesson Worksheet: Density of Solids Mathematics

In this worksheet, we will practice finding the density of a solid and solving word problems involving density.

Question 1

A submarine has a volume of 1,005 cubic feet. Its density must be less than or equal to 62.43 pounds per cubic foot to float on the surface of the water. What is the greatest possible mass that the submarine could have before sinking?

Question 2

A large balloon has a volume of 1.767 cubic feet. It is filled with helium, which has a density of 0.010238 pounds per cubic foot. What is the mass, in pounds and correct to three decimal places, of the helium in the balloon?

Question 3

A right conical piece of metal has base radius 1.8 cm and height 2.7 cm and mass 63 g. Determine the density of the metal to the nearest hundredth.

Question 4

A box-shaped piece of steel of dimensions weighs g. What is its density (i.e., the mass of 1 cm3)?

Question 5

Michael wants to work out the density of the soil in his garden. He fills a tub, with a capacity of 1.5 cubic feet, full of soil and tightly compacts it to remove as much air as he can. He weighs the soil and, after subtracting the mass of the tub, finds it has a mass of 124.5 pounds. What is the density of the soil?

Question 6

Victoria has two rocks of identical mass: one is pumice and the other is lead. One, however, is considerably smaller in volume than the other. Each rock weighs 2 pounds. By displacing water, she finds that one rock has a volume of of 221.48 cubic inches and the other has a volume of 4.88 cubic inches.

Given that lead is denser than pumice, work out the density of pumice. Give your answer to five decimal places.

Work out the density of lead. Give your answer to five decimal places.

Question 7

A model of the Great Pyramid was made using an alloy with a density of 8.5 g/cm3. The model is a square pyramid, with a base length of 9.1 cm, and a height of 6 cm. Determine the mass of the model pyramid in kilograms, approximating your answer to the nearest tenth.

Question 8

A sphere, with a radius of 10 inches, has a mass of 900 pounds. A cylinder, with a radius of 9 inches and a length of 16 inches, has a mass of 890 pounds. Which of the two shapes has the higher density?

• Acylinder
• Bsphere

Question 9

The Density of a material is calculated by dividing its mass by its volume. A particular cylinder has a height of 3 feet, a radius of 2 feet, and a mass of 200 pounds. Calculate the density of the cylinder giving your answer to two decimal places.

Question 10

A cylinder has a radius of 9 feet and a height of 20 feet. It has a mass of 1,100 pounds. Work out, to two decimal places if needed, the density of the cylinder, knowing that density .

This lesson includes 5 additional questions and 18 additional question variations for subscribers.