Question

Popcorn is now available in two different cups at a theater; a square pyramid or a cone. They have the same height of 20 cm. The price of each cup is the same. Which cup is the better deal?

Answer 1

Square pyramid cup is better deal then Cone cup.

Explanation:

Diagram is missing in the question we have attached diagram for your reference.

Given:

height of square pyramid = 20 cm

height of cone = 20 cm

Base of square pyramid = 12 cm

diameter of cone = 12 cm

radius of cone is half of diameter.

radius of cone =
`(diameter)/(2)=(12)/(2) = 6\ cm`

We need to find the which cup is the better deal.

Solution:

We will first find the volume of both cups and then we can say the the one which has greater volume is the better deal in buying.

Volume of square pyramid is calculated by one third times square of the base times height.

framing in equation form we get;

Volume of square pyramid =
`(1)/(3)* 12^2*20= 960\ cm^3`

Now we know that;

Volume of cone is calculated by one third times square of the radius times height times π.

framing in equation form we get;

Volume of cone =
`(1)/(3)\pi r^2h= (1)/(3)\pi* 6^2* 20 \approx 754cm^3`

Now we can see that;

Volume of square pyramid cup which
`960\ cm^3` is greater than Volume of cone cup
`754\ cm^3`

Hence Amount of popcorn will be more in square pyramid cup then in cone cup.

Hence Square pyramid cup is better deal then Cone cup.