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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.

 May 27, 2019
edited by Guest  May 27, 2019

Best Answer 

 #1
avatar+8842 
+3

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

 May 27, 2019
 #1
avatar+8842 
+3
Best Answer

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

hectictar May 27, 2019

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