Volume is the measure of three dimensional space occupied by an object. The volume of the considered rectangular prism is 72π m³
How to find the volume of a right rectangular prism?
Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:
[tex]V = a\times b \times c \: \: \rm unit^3[/tex]
We're specified that:
- Height h of rectangular prism(assuming right rectangular prism) and cylinder = 8 m
- Cross sectional area perpendicular to the height(assumingly) of both are same.
- Rectagular prism's base's dimension is 5 m by x m
- The cylinder has base of 3 m
The cross section of a cylinder (perpendicular to its height) has same area as of its base.
Same goes for cross sectional area of the rectangular prism (perpendicular to its height).
Now, we have:
- Cross sectional area of cylinder = Area of base of cylinder= [tex]\pi (3)^2 = 9\pi \: \rm m^2[/tex]
- Cross sectional area of rectangular prism = Area of base of rectangular prism = [tex]5 \times x \: \rm m^2[/tex]
Cross sectional area of cylinder= Cross sectional area of rectangular prism
Thus, we get:
[tex]9\pi = 5x\\\\\text{Dividing both the sides by 5}\\\\\dfrac{9\pi}{5} = x\\\\\x = \dfrac{9\pi}{5} = 1.8\pi \: \rm m[/tex]
Thus, the volume of the considered right rectangular prism is:
[tex]V = a\times b \times c = 8 \times 5 \times 1.8 \pi = 72 \pi\: \: \rm m^3[/tex]
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