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4 years ago

Help with this question, please!!

Mathematics

1 answer:

Sedaia [141]4 years ago

4 0

Answer:

V = 135π in³
A = 105π in²

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

___

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

___

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

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