Question

A popcorn container is made from a cone with a portion of the cone removed and sealed. The removed portion of the cone has a height of 1/3m . Create an expression, using m , that represents the volume, in cubic centimeters, of the popcorn container.

a) V = 1/3π m³
b) V = 1/3π m³ - 1/9π m²
c) V = 1/3π m²
d) V = 1/3π m² - 1/9π m³

Answer 1

The expression for the volume of the popcorn container, given the portion removed has a height of 1/3m, and converted to cubic centimeters, is V = 1/3π m³ - 1/9π m³.

Step-by-step explanation:

To create an expression for the volume of the popcorn container, which is a cone with a portion removed, we start with the formula for the volume of a cone, which is V = 1/3πr²h. Since the height of the removed portion is 1/3m, the volume of the removed portion is then 1/3π(m/3)²(1/3)m.

Converting meters to centimeters (since 1 meter = 100 centimeters), we get V = 1/3π(100m/3)²(100/3)m = 1/3π(10000/9)m³. To find the volume of the actual container, we subtract the volume of the removed portion from the total volume of the cone. So, the expression using m that represents the volume in cubic centimeters is V = 1/3π m³ - 1/9π m³.