Question

A rectangular prism has a base that is 5 cm by 7 cm and a height of 12 cm. If all dimensions are doubled, what happens to the volume?

Answer 1

Answer:

volume becomes 8 times of original rectangular prism

Step-by-step explanation:

Given dimension of prism : 5 cm by 7 cm and a height of 12 cm

volume of prism is given by = length * width * height

thus volume of given prism = 5*7* 12 cubic cm = 420 cubic units.

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next given that all the dimensions are double

the new dimension are

width = 5*2 cm = 10 cm

length = 7*2 cm = 14 cm

height = 12*2 cm = 24 cm

Volume of new prism = 10*14*24 cubic cm = 3,360 cubic units.

3,360 = 8*420 (420 is volume of original cube)

Thus , volume becomes 8 times of old rectangular prism.

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it can be solved even if we do not have any dimension.

if x,y ,z care dimension of rectangular prism

then its volume = x*y*z cubic  units

now if dimension are doubled then new dimensions are

2x,2y,2z

thus,

new volume = 2x*2y*2z cubic  units = 8xyz cubic units

Thus , we see volume is 8 times of original cube.