We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
38
1
avatar

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+8095 
+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+8095 
+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

21 Online Users

avatar
avatar