A. Patrice buys a block of wax in the shape of a right rectangular prism. The dimensions of the block are 20 cm by 9 cm by 8 cm.
What is the volume of the block? Show your work.
B. Patrice melts the wax and creates a candle in the shape of a circular cylinder that has a diameter of 10 cm and a height of 15 cm.
To the nearest centimeter, what is the volume of the candle? Show your work.
C. Patrice decides to use the remaining wax to create a candle in the shape of a cube.
To the nearest centimeter, what is the length of the side of the cube? Show your work.
+9466 A.
volume of rectangular prism = length * width * height
volume of rectangular prism = 20 cm * 9 cm * 8 cm
volume of rectangular prism = 1440 cm2
B.
volume of circular cylinder = area of circular base * height
volume of circular cylinder = π * radius2 * height
radius = diameter / 2 = 10/2 cm = 5 cm
volume of circular cylinder = π * (5 cm)2 * 15 cm
volume of circular cylinder = π * 25 * 15 cm3
volume of circular cylinder = 375π cm3
volume of circular cylinder ≈ 1178 cm3 (That is to the nearest cubic centimeter.)
C.
volume of remaining wax = volume of rectangular prism - volume of circular cylinder
volume of remaining wax = 1440 cm3 - 375π cm3
volume of remaining wax = ( 1440 - 375π ) cm3
volume of cube = volume of remaining wax = ( 1440 - 375π ) cm3
volume of cube = side * side * side = ( side )3
Equate both representations of volume of cube.
( side )3 = ( 1440 - 375π ) cm3
Take the cube root of both sides of the equation.
side = \(\sqrt[3]{1440-375\pi}\) cm
Plug \(\sqrt[3]{1440-375\pi}\) into a calculator.
side ≈ 6 cm
+9466 A.
volume of rectangular prism = length * width * height
volume of rectangular prism = 20 cm * 9 cm * 8 cm
volume of rectangular prism = 1440 cm2
B.
volume of circular cylinder = area of circular base * height
volume of circular cylinder = π * radius2 * height
radius = diameter / 2 = 10/2 cm = 5 cm
volume of circular cylinder = π * (5 cm)2 * 15 cm
volume of circular cylinder = π * 25 * 15 cm3
volume of circular cylinder = 375π cm3
volume of circular cylinder ≈ 1178 cm3 (That is to the nearest cubic centimeter.)
C.
volume of remaining wax = volume of rectangular prism - volume of circular cylinder
volume of remaining wax = 1440 cm3 - 375π cm3
volume of remaining wax = ( 1440 - 375π ) cm3
volume of cube = volume of remaining wax = ( 1440 - 375π ) cm3
volume of cube = side * side * side = ( side )3
Equate both representations of volume of cube.
( side )3 = ( 1440 - 375π ) cm3
Take the cube root of both sides of the equation.
side = \(\sqrt[3]{1440-375\pi}\) cm
Plug \(\sqrt[3]{1440-375\pi}\) into a calculator.
side ≈ 6 cm
