How does the volume of a rectangular prism change if the width is reduced to 1/10 of its original size, the height is reduced to 1/4 of its original size, and the length is reduced to 2/3 of its original size?
A. V=1/120lwh
B. V=1/60lwh
C. V= 2/3lwh
D. V=3/4lwh
Is it B?
V = L w H
new V = (2/3)L * (1/10) w * (1/4) H
= (2/120) LwH = (1/60) LwH
Yes
original dimensions: l, w, h
volume = lwh
new length --- 2l/3
new width ---- w/10
new height = h/4
new volume + (2l/3)(h/4)(w/10)
= 2 lwh/120
= lwh/60 or (1/60)lwh
so , yes, it is B
Find the volume of the square pyramid. Round your answer to the nearest hundredth.
To find out how the volume of a rectangular prism changes when its dimensions are altered, we can use the formula for volume, which is V = lwh, where l represents the length, w represents the width, and h represents the height.
In this case, we are given that the width is reduced to 1/10 of its original size, the height is reduced to 1/4 of its original size, and the length is reduced to 2/3 of its original size.
To determine the new volume, we need to multiply the new values of the dimensions together.
Let's assume the original width, height, and length are w₀, h₀, and l₀, respectively.
The new width would be 1/10 multiplied by the original width, represented as (1/10)w₀. The new height would be 1/4 multiplied by the original height, represented as (1/4)h₀. Finally, the new length would be 2/3 multiplied by the original length, represented as (2/3)l₀.
Now, we can substitute these values into the volume formula:
V = (1/10)w₀ * (1/4)h₀ * (2/3)l₀
To simplify the expression, we can cancel out the common factors:
V = (1/10) * (1/4) * (2/3) * w₀ * h₀ * l₀
V = (1/120) * w₀ * h₀ * l₀
Therefore, the new volume of the rectangular prism, when the dimensions are reduced as given, can be expressed as V = 1/120lwh.
Thus, option A, V = 1/120lwh, is the correct answer.