424 algebra De mystif ieD
The volume of a box is 72 cm^3. Its height is 3 cm. Its length is 1.5 times its
width. What are the length and width of the box?
The formula for the volume of the box is V = LWH. The volume is 72, the
height is 3 and the length is 1.5 times the width (L = 1.5W) so the formula
becomes 72 (= 15 .)WW() 3. We now solve this equation for W.72 15 3
72 45
72
45
16
4222=
===
=(. )()
..WW
WWW
WThe box’s width is 4 cm and its length is (1.5)(4) = 6 cm.The surface area of a ball is 314 in^2. What is the ball’s diameter?
The formula for the surface area of a sphere is SA = 4 or^2. The area is 314, so
the formula becomes 314 = 4or^2.314 4
314
4
314
4
522===≈ooorrrrThe radius of the ball is approximately 5 inches. The diameter is twice the
radius, so the diameter is approximately 10 inches.The manufacturer of a drinking cup that is 6 inches tall is considering
increasing its radius. The cup has straight sides (the top is the same size as
the bottom). If the radius is increased by 1 inch, the new volume would be
169.6 in^3. What is the cup’s current radius?
The formula for the volume of a right circular cylinder is V = or^2 h. The cup’s
height is 6. If the cup’s radius is increased, the volume would be 169.6.