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Chapter 1: Q57. (page 20)

Make a rough estimate of the volume of your body (inm3).

Short Answer

Expert verified

The volume of your body is approximately 8×10-2m3.

Step by step solution

01

Step 1. Definition of a rough estimate

A rough estimate is an approximate calculation of a quantity or a number.

02

Step 2. Definition of volume

Volume is defined as the amount of space occupied by a solid 3-D figure like a cuboid, cylinder, or sphere.

03

Step 3. Assumptions to determine the volume of a human body

Assume that your body is a perfect cylinder with the dimensions corresponding to your body (tall and approx. 30-inch waist).

Thus, the cross-sectional radius (r) will be 0.12m.

The height (h) of the cylinder will be 1.70m.

04

Step 4. Determination of the volume of the cylinder

The volume of a regular cylinder is V=πr2h.

Substitute the numerical values in the above expression.

V=3.140.12m21.70m=0.07690m3≈8×10-2m3

Thus, the volume of the body is roughly 8×10-2m3.

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Most popular questions from this chapter

Three students derive the following equations, in which x refers to the distance traveled, v refers to the speed, a is the acceleration (m·s-2), t is the time, and the subscript zero (role="math" localid="1643793406182" 0) means a quantity at a time t = 0. Here are their equations: (a)x=vt2+2at, (b)x=v0t+12at2, and (c)x=v0t+2at2. Which of these could possibly be correct according to dimensional check, and why?

How big is a ton? That is, what is the volume of something that weighs a ton? To be specific, estimate the diameter of a 1-ton rock, but first make a wild guess: will it be 1 ft across, 3 ft, or the size of a car? [Hint: Rock has mass per volume about 3 times that of water, which is 1 kg per liter103cm3or 62 lb per cubic foot.]

The following formula estimates an average person’s lung capacity V(in litres, where1L=103cm3):

V=4.1H-0.018A-2.7,

Where H and A are the person’s height (in metres) and age (in years) respectively. In this formula, what are the units of the numbers 4.1, 0.018, and 2.7?

Which is not true about an order-of-magnitude estimation?

(a) It gives you a rough idea of the answer.

(b) It can be done by keeping only one significant figure.

(c) It can be used to check if an exact calculation is reasonable.

(d) It may require making some reasonable assumptions in order to calculate the answer.

(e) It will always be accurate to at least two significant figures.

What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radiusr=0.84±0.04m?
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