Answer:
C.
[tex]V = \pi * 5^2(13) +\frac{1}{3}\pi * 5^2 (12)[/tex]
Step-by-step explanation:
Given:
The figure is a combination of a cone and a cylinder
Radius (of both), [tex]r = 5[/tex]
Height of Cylinder, [tex]H_1 = 13[/tex]
Height of Cone, [tex]H_2 = 25 - 13 = 12[/tex]
Required:
Volume of the figure
Let V represents the volume of the figure;
[tex]V_1[/tex] represents the volume of the cylinder
[tex]V_2[/tex] represents the volume of the cone
So, [tex]V = V_1 + V_2[/tex]
Where [tex]V_1 = \pi r^2H_1[/tex] and [tex]V_2 = \frac{1}{3}\pi r^2 H_2[/tex]
So, V becomes
[tex]V = \pi r^2H_1 + \frac{1}{3}\pi r^2 H_2[/tex]
Factorize the above expression
[tex]V = \pi r^2(H_1 + \frac{1}{3}H_2)[/tex]
Substitute [tex]r = 5[/tex]; [tex]H_1 = 13[/tex];[tex]H_2 = 12[/tex]
[tex]V = \pi * 5^2(13 + \frac{1}{3} * 12)[/tex]
[tex]V = \pi * 5^2(13 + \frac{1}{3} * 12)[/tex]
Open Bracket
[tex]V = \pi * 5^2(13) +\pi * 5^2 \frac{1}{3} (12)[/tex]
Reorder
[tex]V = \pi * 5^2(13) +\frac{1}{3}\pi * 5^2 (12)[/tex]
From the list of options given, option c is correct.
