This topic focuses on deriving volume formulas for several three-dimensional shapes such as rectangular pyramids, cones, and spheres. The problems involve recognizing and applying the correct formula based on the dimensions provided for each shape. The math skills practiced include understanding geometric formulas for volume and applying these formulas to solve specific geometrical problems related to complex 3D shapes. This is part of a larger unit aimed at introducing the volume and surface area of complex 3D shapes in a geometrical context.

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Volume - All - Words to Formula Worksheet

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Volume - All - Words to Formula
1
What is the formula for the volume of this shape?
A Sphere with radius 4
a A LaTex expression showing V = 4 over 3 Pi r to the power of 3
b A LaTex expression showing V = 4 Pi r to the power of 2
2
A Rectangular Pyramid with a base of 2 by 5 and a height of 3
What is the formula for the volume of this shape?
a A LaTex expression showing V = lwh over 3
b A LaTex expression showing V = lw + l square root of (w over 2 ) to the power of 2 + h to the power of 2 + w square root of (l over 2 ) to the power of 2 + h to the power of 2
3
What is the formula for the volume of this shape?
A Sphere with radius 5
a A LaTex expression showing V = Pi r to the power of 2 h
b A LaTex expression showing V = 4 over 3 Pi r to the power of 3
4
What is the formula for the volume of this shape?
A Cone with radius 2 and a height of 3
a A LaTex expression showing V = Pi r to the power of 2 h
b A LaTex expression showing V = 1 over 3 h Pi r to the power of 2
5
What is the formula for the volume of this shape?
A Cone with radius 5 and a height of 2
a A LaTex expression showing V = Pi r (r + square root of h to the power of 2 + r to the power of 2 )
b A LaTex expression showing V = 1 over 3 h Pi r to the power of 2
6
What is the formula for the volume of this shape?
A Cylinder with radius 5 and height 4
a A LaTex expression showing V = 2 Pi r h + 2 Pi r to the power of 2
b A LaTex expression showing V = Pi r to the power of 2 h
7
A Rectangular Pyramid with a base of 4 by 2 and a height of 3
What is the formula for the volume of this shape?
a A LaTex expression showing V = lwh over 3
b A LaTex expression showing V = lw + l square root of (w over 2 ) to the power of 2 + h to the power of 2 + w square root of (l over 2 ) to the power of 2 + h to the power of 2
8
A Rectangular Pyramid with a base of 2 by 3 and a height of 4
What is the formula for the volume of this shape?
a A LaTex expression showing V = lw + l square root of (w over 2 ) to the power of 2 + h to the power of 2 + w square root of (l over 2 ) to the power of 2 + h to the power of 2
b A LaTex expression showing V = lwh over 3