Mathematics: Abox has dimensions l, w, and h. how is the volume changed if the length and width are each multiplied by 5 and the height remains the same?

Abox has dimensions l, w, and h. how is the volume

jakalenn2018

06.04.2021

Option B.

Step-by-step explanation:

It is given that the cross sectional areas of a right triangular prism and a right cylinder are congruent.

Height of right triangular prism = 2 units.

Height of cylinder = 6 units.

Let area of cross section of right triangular prism and right cylinder is A square units.

So,

Volume of right triangular prism is

$V_1=\text{Cross section area}\times \text{Height}=2A\text{ cubic units}$

Volume of cylinder is

$V_2=\text{Cross section area}\times \text{Height}=6A\text{ cubic units}$

Here,

$3\times 2A=6A$

$3\times V_1=V_2$

$V_1=\dfrac{1}{3}V_2$

The volume of a triangular prism is one third of the volume of a cylinder.

The volume of a triangular prism is not equal to the volume of a cylinder.

Therefore, the correct option is B.

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