Question

A 1.8 m tall man has a waistline of 100 cm. Which measure best approximates the volume of the man when using a cylinder to approximate the man's shape? Question 1 options:

0.06 m³
0.14 m³
0.4 m³
0.72 m³

Answer 1

Given height of the man = 1.8 m

and waistline = 100 cm = 1 m.

Consider the shape of the man cylindrical.

Waistline of the man = circumference of the circular base of cylinder = 1 m

`\Rightarrow 2\pi r = 1 \\ \Rightarrow r = (0.5)/(\pi)`

Volume of Cylinder ,
`V = \pi r^2h`

`\Rightarrow V = \pi* ((0.5)/(\pi) )^2* 1.8 \\ \\ \Rightarrow V = (0.25)/(\pi) * 1.8 = (0.45)/(\pi) \approx0.14 \: m^3`.

Hence, Volume of the man when using a cylinder is
`0.14\: m^3`

second option is the correct choice.

Answer 2

waistline 100cm is the circle circumference->calculate radius
100cm=1m=2*r*π
0.5=r*π
0.5/π=r

area of a circle: A=r²π=(0.5/π)²π=0.25/π m²

circlearea*height=cylinder volume

1.8*0.25/π=0.45/π m³~0.143239 m³
so the second option is the correct one