Question

Crystal was told by her mom she could get one scoop of candy. There are two scoops and both scoops are shaped like cones. Given the dimensions below which cone should Crystal use if she wants to get the greatest amount of candy?
Cone A:
30 cm
15 cm
15cm
Cone B:
15 cm
30cm
7.5 cm

Answer 1

To determine which cone will provide the greatest amount of candy, we need to calculate the volume of each cone. The formula for the volume \( V \) of a cone is given by:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius of the base and \( h \) is the height of the cone.

Now, let's calculate the volume for each cone based on the provided dimensions.

### Cone A:
- Height (\( h \)) = 30 cm
- Radius (\( r \)) = 15 cm

Using the volume formula:
\[
V_A = \frac{1}{3} \pi (15^2)(30)
\]
\[
V_A = \frac{1}{3} \pi (225)(30)
\]
\[
V_A = \frac{1}{3} \pi (6750)
\]
\[
V_A = 2250\pi \quad \text{cm}^3
\]

### Cone B:
- Height (\( h \)) = 15 cm
- Radius (\( r \)) = 7.5 cm

Using the volume formula:
\[
V_B = \frac{1}{3} \pi (7.5^2)(15)
\]
\[
V_B = \frac{1}{3} \pi (56.25)(15)
\]
\[
V_B = \frac{1}{3} \pi (843.75)
\]
\[
V_B = 281.25\pi \quad \text{cm}^3
\]

### Comparison:
Now, we can directly compare the simplified volumes:

- Volume of Cone A: \( 2250\pi \quad \text{cm}^3 \)
- Volume of Cone B: \( 281.25\pi \quad \text{cm}^3 \)

Since \( 2250\pi \) is much greater than \( 281.25\pi \), **Cone A** provides the greatest amount of candy.

### Conclusion:
Crystal should use **Cone A** to get the greatest amount of candy.