Answer:
Step-by-step explanation:
Area of a circle is ...
A = πr² . . . r is the radius
Area of a sphere is ...
A = 4πr²
Lateral area of a cylinder is ...
A = πdh = 2πrh . . . h is the height
Volume of a cylinder is ...
V = πr²h
Volume of a sphere is ...
V = (4/3)πr³
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The area of the composite figure is the sum of the areas ...
total area = base circle area + cylinder lateral area + 1/2 sphere area
= πr² + 2πrh + (1/2)4πr² = (πr)(r +2h +2r)
= πr(3r +2h)
For the given dimensions, r=3 in, h = 13 in, this is ...
total area = π(3 in)((3·3 +2·13) in) = 105π in²
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The volume of the composite figure is the sum of the volumes ...
total volume = cylinder volume + 1/2 sphere volume
= πr²h + (1/2)(4/3)πr³ = πr²(h + 2/3r)
= π(3 in)²((13 +2/3·3) in) = 135π in³
