Question

find the surface area of the composite solid, where the top is a hemisphere, in terms of pi 24 mm 18 mm 1512π mm² 1836π mm² 2160π mm² 2808π mm²

Explanation:

Step1: Find surface - area of hemisphere

The surface - area of a hemisphere is $2\pi r^{2}$. Given $r = 18$ mm, so $A_{hemisphere}=2\pi(18)^{2}=2\pi\times324 = 648\pi$ mm².

Step2: Find lateral surface - area of cylinder

The lateral surface - area of a cylinder is $2\pi rh$. Here, $r = 18$ mm and $h = 24$ mm. So $A_{lateral}=2\pi\times18\times24=864\pi$ mm².

Step3: Find base area of cylinder

The base area of a cylinder is $\pi r^{2}$. With $r = 18$ mm, $A_{base}=\pi(18)^{2}=324\pi$ mm².

Step4: Calculate total surface area of composite solid

The total surface area $A$ of the composite solid is the sum of the surface - area of the hemisphere, the lateral surface - area of the cylinder, and the base area of the cylinder. $A=A_{hemisphere}+A_{lateral}+A_{base}=648\pi + 864\pi+324\pi=1836\pi$ mm².

Answer:

B. $1836\pi$ mm²