Problem Set #1-21

Geometery

Angles, Shapes, Areas and Volumes

Problem 1

• Calculate the volume of a rectangular solid.

• Eq: V = l x w x h

• Sub: V = 25.5 cm x 20.0 cm x 35.0 cm

• Ans: 17,850 cm^3 *

• * The use of the caret, ^, symbol in this situation indicates that the number that follows is intended to be an exponent.

Problem 2

• Calculate the volume of a cylinder.

• Eq: V = x r^2 x h *

• Sub: V = 3.14 x (24 cm / 2)^2 x 50 cm.

• Ans: V = 22,608 cm^3

• * A radius is 1/2 of a given diameter.

Problem 3

• Calculate the volume of a sphere.

• Eq: 4 x x r^3 / 3

• Sub: 4 x 3.14 x (10 cm / 2)^3 / 3

• Ans: 523.3 cm^3

Problem 4

• Calculate the volume of a cone.

• Eq: V = x r^2 x h / 3

• Sub: V = 3.14 x (24 cm / 2)^2 x 48 cm / 3

• Ans: V = 7,234 cm^3

Problem 5

• Calculate the radius of a sphere.• Eq: V = 4 x x r^3 / 3• and r = (3 x V / 4 x )^(1/3)• Sub: r = (3 x 1000 cm^3 / 4 x 3.14)^(1/3)• Ans: 6.20455 cm• Note: in some graphing calculators we• suggest the use of the parentheses as in• r = ((3*1000)/(4*))^(1/3)