The expression that represents the volume of the composite figure is [tex]\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)[/tex]. The correct option is the third option [tex]\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)[/tex]
From the question, we are to determine the expression that represents the volume of the composite figure
The composite figure consist of a cylinder and a cone
∴ Volume of the composite figure = Volume of the cylinder + Volume of the cone
Volume of a cylinder = [tex]\pi r^{2} h[/tex]
Where r is the radius
and h is the height of the cylinder
Volume of a cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
Where r is the radius
and h is the height of the cone
Consider the composite figure
For the cylinder part
r = 5
h = 13
For the cone part
r = 5
h = 25 - 13 = 12
Thus,
Volume of the composite figure = [tex]\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)[/tex]
Hence, the expression that represents the volume of the composite figure is [tex]\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)[/tex]. The correct option is the third option [tex]\pi (5^{2})(13) + \frac{1}{3} \pi (5^{2})(12)[/tex]
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