Question Video: Finding an Expression for the Cross-Sectional Area of a Prism | Nagwa Question Video: Finding an Expression for the Cross-Sectional Area of a Prism | Nagwa

Question Video: Finding an Expression for the Cross-Sectional Area of a Prism Mathematics • First Year of Preparatory School

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Find an expression for the shaded cross-sectional area of the following rectangular prism.

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Video Transcript

Find an expression for the shaded cross-sectional area of the following rectangular prism.

In this question, we want to find an expression for the cross-sectional area of a given rectangular prism. To do this, we are given an expression for the volume of the prism and an expression for its height.

We can begin by recalling that the volume of a prism is given by the area of its cross section multiplied by its height. We can substitute the given expressions for the volume and height into the formula for the volume of a prism to obtain 240𝑦𝑧 squared is equal to 𝑏 times 15𝑦. We want to find the cross-sectional area 𝑏. So, we will need to divide both sides of the equation through by 15𝑦. This gives us that 𝑏 is equal to 240𝑦𝑧 squared over 15𝑦, where we note that 𝑦 is nonzero.

We can now cancel the shared factor of 15 and the shared factor of 𝑦 in the numerator and denominator. This gives us that the cross-sectional area of the given rectangular prism is 16𝑧 squared.

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