Question

1. A house is 42.0 ft long and 38.0 ft wide and has 8.0-ft-high ceilings. What is the volume of the interior of the house in cubic meters and cubic centimeters?

_________ m^3

_________ cm^3

2. An auditorium measures 45.0 m ✕ 30.0 m ✕ 7.0 m. The density of air is 1.20 kg/m³.

(a) What is the volume of the room in cubic feet?

_________ ft^3

(b) What is the weight of air in the room in pounds?

_________ lb

3. How many significant figures are in the following numbers?

(a) 190.0 ± 0.4

___________

(b) 8.00 ✕ 10¹⁴
___________

(c) 4.60 ✕ 10^-9

___________
(d) 0.0065

___________

4. For the right triangle shown in the figure below, what are each of the following? (Let  y = 3.60 m and r = 3.90 m.)

A diagram of a right triangle with a hypotenuse labeled r, one leg labeled x and the other leg labeled y. The angle adjacent to x is labeled θ and the angle adjacent to y is labeled ϕ.

(a) the length (in m) of the unknown side x

__________m

(b) the tangent of θ

__________

(c) the sine of ϕ

_________

(d) What if? Keeping the length found in (a) fixed, by what factor would the length of the 3.60 m side have to be changed for the angles θ and ϕ to be equal? (Let y' be the new length of the 3.60 m side.)

y'

y

= ___________

Answer 1