Question

exam 13
question 1: standard g.gmd.3
volume is how many dimensions?
a. 2
b. 1
c. 3
d. 4
question 2: standard g.gmd.3
generally volume is the area of the base of the shape multiplied by _____.
a. width
b. height
c. radius
d. pi
question 3: standard g.gmd.3
which option shows the formula for volume of cylinder?
a. $v = \pi r^2 h$
b. $v = (\pi r^2 h)/3$
c. $v = (\text{area}_{\text{base}} h)/3$
d. $v = (4/3)\pi r^3$
question 4: standard g.gmd.3
if the radius of a cylinder is 4 inches and the height is 3 inches, what is the volume?
a. 50.3
b. 42.8
c. 120.5
d. 150.8
question 5: standard g.gmd.3
which is the correct formula for volume of a sphere?
a. $v = \pi r^2 h$
b. $v = (\pi r^2 h)/3$
c. $v = (\text{area}_{\text{base}} h)/3$
d. $v = (4/3)\pi r^3$

Explanation:

Question 1

Volume measures the space occupied in three - dimensional space. So it has 3 dimensions.

The general formula for the volume of a prism - like shape is \(V=\text{Area of base}\times\text{height}\). For example, in a cylinder, volume is the area of the circular base (\(\pi r^{2}\)) times the height (\(h\)).

The base of a cylinder is a circle with area \(\pi r^{2}\). The volume of a cylinder is the area of the base times the height (\(h\)), so the formula is \(V = \pi r^{2}h\). Option b is the formula for the volume of a cone, option c is also related to a cone (or pyramid) and option d is the formula for the volume of a sphere.

Answer:

c. 3

Question 2