Question

1. what is the first step in calculating the volume of a cone?

a. calculate the area of the base
b. divide the radius by the height
c. multiply the radius by the height
d. multiply the height by π

if the height of a cone is 10 cm and the radius is 5 cm, what is the area of the base?
a. 5π square cm
b. 10π square cm
c. 100π square cm
d. 25π square cm

which of the following is an example of a cone used in a practical scenario?
a. cube
b. sphere
c. cylinder
d. traffic cone

what is the shape of the base of a cone?
a. square
b. circle
c. rectangle
d. triangle

what is the term for the straight line distance from the base to the tip of the cone?
a. diameter
b. radius
c. height
d. slant height

in the formula for the volume of a cone, what does the variable r represent?
a. height of the cone
b. radius of the base
c. slant height of the cone
d. volume of the cone

how can the volume of a cone be described compared to a cylinder with the same base and height?
(option not fully visible)

Explanation:

Step1: Analyze cone volume formula

The volume of a cone is $V=\frac{1}{3}Bh$, where $B$ is base area.

Step2: Solve base area for given cone

Base area $B=\pi r^2$, $r=5$ cm, so $B=\pi(5)^2=25\pi$.

Step3: Match practical cone example

Identify real-world cone shape.

Step4: Recall cone base shape

A cone has a circular base.

Step5: Define cone height term

Straight line from base to tip is height.

Step6: Identify variable $r$ in volume formula

In $V=\frac{1}{3}\pi r^2h$, $r$ is base radius.

Step7: Relate cone and cylinder volume

Cone volume is $\frac{1}{3}$ of same base/height cylinder.

Answer:

1. a. Calculate the area of the base
2. d. 25π square cm
3. d. Traffic cone
4. b. Circle
5. c. Height
6. b. Radius of the base
7. (Completed option: The volume of the cone is $\frac{1}{3}$ the volume of the cylinder with the same base and height)