Question

an ice cream shop sells ice cream in waffle cones and waffle bowls. the waffle bowls are in the shape of a cylinder. the dimensions of the cones and bowls are shown below. mark each statement as true or false.
a. the diameter of the waffle cone is half the diameter of the waffle bowl.
b. the area of the base of the waffle bowl is twice the area of the base of the waffle cone.
c. the volume of the waffle bowl is about 443 cm³ greater than the volume of the waffle cone.

Explanation:

Step1: Evaluate statement a

First, find diameters:
Cone diameter: $d_{cone} = 2 \times 3 = 6$ cm
Bowl diameter: $d_{bowl} = 2 \times 5 = 10$ cm
Half the bowl's diameter: $\frac{10}{2} = 5$ cm
Since $6
eq 5$, the statement is false.

Step2: Evaluate statement b

Calculate base areas:
Cone base area: $A_{cone} = \pi r^2 = \pi \times 3^2 = 9\pi$ cm²
Bowl base area: $A_{bowl} = \pi r^2 = \pi \times 5^2 = 25\pi$ cm²
Twice the cone's base area: $2 \times 9\pi = 18\pi$ cm²
Since $25\pi
eq 18\pi$, the statement is false.

Step3: Evaluate statement c

Calculate volumes:
Cone volume: $V_{cone} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi \times 3^2 \times 8 = 24\pi \approx 75.4$ cm³
Bowl (cylinder) volume: $V_{bowl} = \pi r^2 h = \pi \times 5^2 \times 5 = 125\pi \approx 392.7$ cm³
Since $392.7 < 443$ and $392.7 > 75.4$, the claim about the value is wrong, so the statement is false.

Answer:

a. False
b. False
c. False