Question

1. the area of the circular base is calculated using which formula?

a. $a = \pi r^2$
b. $a = \pi d^2$
c. $a = \pi dh$
d. $a = 2\pi r$

1. a cylindrical container with a radius of 3 cm and height of 20 cm is filled with water. what is the volume of water it holds?

a. $60\pi\\ \text{cm}^3$
b. $180\pi\\ \text{cm}^3$
c. $90\pi\\ \text{cm}^3$
d. $270\pi\\ \text{cm}^3$

1. what is an acceptable choice of unit for measuring the volume of a cylinder?

a. meters
b. centimeters
c. grams
d. liters

1. what is the primary difference between the volume formulas of a cylinder and a cone?

a. the cone formula includes the diameter
b. the cylinder formula does not include $\pi$
c. the cone formula includes a factor of $\frac{1}{3}$
d. the cylinder formula uses the height squared

1. a cylinder has a height of 10 cm and a volume of $100\pi\\ \text{cm}^3$. what is the radius of the cylinder?

a. 7.07 cm
b. 5 cm
c. 6.34 cm
d. 4.07 cm

1. the radius of a cylinder is doubled while the height remains the same. how does the volume change?

a. it decreases
b. it stays the same
c. it doubles
d. it quadruples

Explanation:

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Question 1

Step1: Recall circle area formula

The area of a circle is given by $A=\pi r^2$, where $r$ is radius.

Question 2

Step1: Recall cylinder volume formula

Volume $V=\pi r^2 h$

Step2: Substitute $r=3, h=20$

$V=\pi \times 3^2 \times 20 = \pi \times 9 \times 20 = 180\pi$

Question 3

Meters and centimeters are units of length, grams are units of mass. Liters are a standard unit for measuring volume.

Question 4

Cylinder volume: $V_{cylinder}=\pi r^2 h$; Cone volume: $V_{cone}=\frac{1}{3}\pi r^2 h$. The only key difference is the $\frac{1}{3}$ factor in the cone formula.

Answer:

b. $A = \pi r^2$

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