Volume Formulas
Common Core (Geometry)
Common Core for Mathematics
Examples, solutions, videos, and lessons to help High School students learn how to use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Common Core: HSG-GMD.A.3
Volume of Cylinder and Rectangular Prisms (word problem) - Geometry
This video focuses on solving a volume of solids word problem. In particular, the volume of a rectangular prism and cylinder are used to solve the volume of solids word problem.
Example:
Farmer Babel's favorite pig is Hadley, but she has constipated for two days. To help Hadley, Babel pours prune juice into a 5 ft x 3 ft x 2 ft rectangular feeding tub. If the prune juice comes in cylindrical bottles with a radius of 0.5 ft and a height of 1.8 ft, how many bottles will Babel need to fill the tub completely?
Example:
The cylinder is melted down into a sphere of radius r. Find an expression for r in terms of x.
Examples:
1) How many square bales contain the same amount of hay as one round bale?
2) How many cubic cm of wax are needed to make the crayon?
3) What is the approximate volume of each balloon? Pyramid and Cylinder Word Problem.
Example:
An iron weight in the shape of a square based pyramid with base 10 cm by 10 cm and height 14 cm is placed inside a cylindrical container of radius 12 cm and height 40 cm. The container is then filled to the brim with water and the weight is taken out. By how much will the water level drop? (use π = 3.142) Volumes of Pyramids, Cones, and Spheres
How to solve problems involving the volumes of pyramids, cones, and spheres?
Example:
The pyramid has the same base and height as the cube that contains it. What is the difference between the volume of the cube and the volume of the pyramid? Dimensions are in cm. How to calculate the volume of a cone and hemisphere?
Example:
The cone is 10cm tall and 12cm at the base; it's attached to a hemisphere (half a ball) and you are asked to calculate the volume.
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