Question

question 1-12 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 2106π mm² 2808π mm²

Explanation:

Step1: Calculate hemisphere surface area

Use formula \(A_{hemisphere}=2\pi r^{2}\), \(r = 18\), so \(A_{hemisphere}=2\pi\times(18)^{2}=648\pi\)

Step2: Calculate cylinder lateral surface area

Use formula \(A_{lateral}=2\pi r h\), \(r = 18\), \(h = 24\), so \(A_{lateral}=2\pi\times18\times24 = 864\pi\)

Step3: Calculate cylinder base area

Use formula \(A_{base}=\pi r^{2}\), \(r = 18\), so \(A_{base}=\pi\times(18)^{2}=324\pi\)

Step4: Calculate total surface area

\(A=A_{hemisphere}+A_{lateral}+A_{base}=648\pi + 864\pi+324\pi=1836\pi\)

Answer:

1. First, analyze the composite solid. It consists of a hemisphere on top of a cylinder.

• For the hemisphere:
• The radius \(r = 18\) mm. The surface - area formula for a hemisphere is \(A_{hemisphere}=2\pi r^{2}\).
• Substitute \(r = 18\) mm into the formula: \(A_{hemisphere}=2\pi\times(18)^{2}=2\pi\times324 = 648\pi\) \(mm^{2}\).
• For the cylinder:
• The formula for the lateral - surface area of a cylinder is \(A_{lateral}=2\pi r h\), and the area of the bottom - base of the cylinder is \(A_{base}=\pi r^{2}\). Here, \(r = 18\) mm and \(h = 24\) mm.
• The lateral - surface area \(A_{lateral}=2\pi\times18\times24=864\pi\) \(mm^{2}\), and the area of the bottom - base \(A_{base}=\pi\times(18)^{2}=324\pi\) \(mm^{2}\).
• The total surface area of the composite solid \(A = A_{hemisphere}+A_{lateral}+A_{base}\).
• \(A=648\pi + 864\pi+324\pi\).
• Combine like terms: \(A=(648 + 864+324)\pi=1836\pi\) \(mm^{2}\).

So the answer is \(1836\pi\) \(mm^{2}\).