Q: A steel sheet has dimensions $$102\ \mathrm{cm} by$$ $$67\ \mathrm{cm}. $$What is the area in $$\mathrm{m}^2$$ with the correct significant figures and in engineering notation?

$$6.83 \times 10$$^{-1}$$\ \mathrm{m}^2$$

Question 1

Suppose your car can travel 34.5 miles on 1.03 gallons of fuel. If you have 14.3 litres of fuel, how many kilometers can your car travel? (1 mile = 1.609 km, 1 gallon = 3.785 L)

Accepted Answer

$$203.6\ \mathrm{km}$$

Question 2

How many litres of fuel would be required to drive a distance equal to the circumference of the Earth ($$40,075\ \mathrm{km}) in $$the car described above?

Accepted Answer

$$2814.3\ \mathrm{L}$$

Question 3

A square floor has sides of $$3.5\ \mathrm{m}. If $$you use tiles that are $$0.45\ \mathrm{m} on a $$side, how many tiles are needed to cover the floor? Assume you cannot cut tiles.

Accepted Answer

$$64$$

Question 4

You want to water a lawn of area $$0.330\ \mathrm{acre} to a $$depth of $$1.00\ \mathrm{mm}. $$How much water is needed in cubic meters? ($$1\ \mathrm{acre} = 4046.86\ \mathrm{m}^2)$$

Accepted Answer

$$1.335\ \mathrm{m}^3$$

Question 5

If the volume of a water droplet is $$0.00550\ \mathrm{mL}$$, how many drops are needed to water the lawn above?

Accepted Answer

$$242,811,600$$

Question 6

A trail rises $$120\ \mathrm{m}$$ over a horizontal distance of $$1.0\ \mathrm{km}. $$What is the slope of the trail?

Accepted Answer

$$0.12$$

Question 7

A steel sheet has dimensions $$102\ \mathrm{cm} by$$ $$67\ \mathrm{cm}. $$What is the area in $$\mathrm{m}^2$$ with the correct significant figures and in engineering notation?

Accepted Answer

$$6.83 	imes 10$$^{-1}$$\ \mathrm{m}^2$$

Question 8

A rectangular field is $$282\ \mathrm{m}$$ long and $$189\ \mathrm{m}$$ wide. If a mower moves at $$4.0\ \mathrm{km/h}$$ and has a cutting width of $$2.4\ \mathrm{m}$$, how long will it take to mow the field assuming straight, parallel passes along the length?

Accepted Answer

$$3.53\ \mathrm{hours}$$

Question 9

A cylindrical tank has a diameter of $$1.2\ \mathrm{m}$$ and a height of $$1.5\ \mathrm{m}. If a $$solid sphere of diameter $$0.9\ \mathrm{m} is $$submerged in the tank, how much water spills out?

Accepted Answer

$$0\ \mathrm{L}$$

Question 10

Which of the following numbers has 3 significant figures?

Accepted Answer

$$0.435$$

Question 11

If you want to express the number $$12,790 in $$engineering notation with no units, which is the correct answer?

Accepted Answer

$$1.279 	imes 10^4$

Question 12

A steel sheet has dimensions $$102\ \mathrm{cm} by$$ $$67\ \mathrm{cm}. $$How many significant figures should the area have?

Accepted Answer

3

Question 13

If a tile is $$0.45\ \mathrm{m} on a $$side, what is its area in $$\mathrm{m}^2$$?

Accepted Answer

$$0.2025\ \mathrm{m}^2$$

Question 14

A sphere has a diameter of $$0.9\ \mathrm{m}. $$What is its volume in $$\mathrm{m}^3$$?

Accepted Answer

$$0.381\ \mathrm{m}^3$$

Question 15

If you need to water a lawn of $$0.330\ \mathrm{acre} to a $$depth of $$1.00\ \mathrm{mm}$$, and each drop is $$0.00550\ \mathrm{mL}$$, how many drops are needed? (1 acre = $$4046.86\ \mathrm{m}^2)$$

Accepted Answer

$$242,811,600$$

Question 16

A commercial mower moves at $$4.0\ \mathrm{km/h}$$ and has a cutting width of $$2.4\ \mathrm{m}. If $$the field is $$282\ \mathrm{m} by$$ $$189\ \mathrm{m}$$, how many passes are needed along the length?

Accepted Answer

$$118$$

Question 17

What is the formula for the volume of a cylinder with diameter $$D$$ and height $$H$$?

Accepted Answer

$$V = \frac{\pi D^2$}{4} H$$

Question 18

If you have $$14.3\ \mathrm{L} of $$fuel and your car's fuel efficiency is $$9.42\ \mathrm{km/L}$$, what is the maximum distance you can travel?

Accepted Answer

$$203.6\ \mathrm{km}$$

Physics Fundamentals: Unit Conversions, Significant Figures, and Applied Problem Solving

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