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Volume word problems with cones, cylinders, and spheres
Description
Exercise Name: Volume word problems with cones, cylinders, and spheres
Math Missions: 8th grade (U.S.) Math Mission, High school geometry Math Mission
Types of Problems: 4

The Volume word problems with cones, cylinders, and spheres exercise appears under the 8th grade (U.S.) Math Mission and High school geometry Math Mission. This exercise uses geometric volume formulas to solve word problems.

## Types of Problems

There are four types of problems in this exercise:

1. Use the volume of a cone: This problem describes a word problem that relies on the volume of a cone. The user is asked to find the correct answer and write it in the space provided.
2. Use the volume of a cylinder: This problem describes a word problem that relies on the volume of a cylinder. The user is asked to find the correct answer and write it in the space provided.
3. Use the volume of a sphere: This problem describes a word problem that relies on the volume of a sphere. The user is asked to find the correct answer and write it in the space provided.
4. Use the volumes of various geometric solids: This problem calls upon some combination of cone, cylinder and sphere formulas to solve a problem.

## Strategies

Knowledge of the volume formulas can be considered vital to performing this problem accurately and efficiently.

1. The volume of a cone is ${\frac{1}{3}\times\pi\times r^2\times h}$.
2. The volume of a cylinder is ${\pi\times r^2\times h}$, the volume of the cone multiplied by three.
3. The volume of a sphere is ${\frac{4}{3}\times\pi\times r^3}$.

## Real-life applications

1. Volume formulas are useful in the calculus for understand some of the beginning integral applications.
2. Architects use lots of geometry when building bridges, roofs on houses, and other structures.
3. Spheres are common shapes in nature when gravity is allowed to act freely (planets, raindrops, etc.)
4. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.
5. When one fills up their vehicle with gas, the volume of gasoline in their gas tank helps to determine their purchase. Whether they fill up with gallons or liters of gasoline or diesel, the amount is a volume calculation. On a smaller scale, when one fills up a gas can to take to another vehicle or to use the gas to power another device, they again use volume for measuring.