Question

A shop sells 2 brands of sunflower seeds. Brand A's package is in the shape of a cone with a radius of 3.5 centimeters and height 8 centimeters. Brand B's package is in the shape of a square prism. The prism's height is 3.5 centimeters, and each side of the base measures 4 centimeters. Which package contains more seeds? Explain or show your reasoning.

Answer 1

Calculating the volumes, Brand A's cone-shaped package has a volume of approximately 103.67 cm³, and Brand B's square prism package has a volume of 56 cm³. Hence, Brand A's package contains more seeds.

Step-by-step explanation:

To determine which package contains more seeds, we need to calculate the volume of both packages. Brand A has a cone-shaped package with a radius of 3.5 centimeters and height 8 centimeters. The volume of a cone is given by ⅓πr²h. For Brand A, the volume VA is:

VA = ⅓π(3.5)2(8) = ⅓π(12.25)(8) = ⅓π×98 = approximately 103.67 cm³ (after rounding to two significant figures as per the measurement of the radius).

Brand B's package is a square prism with a height of 3.5 centimeters and a base side of 4 centimeters. The volume of a prism is the area of the base times the height. The area of the square base AB is:

AB = side² = 4² = 16 cm²

The volume VB is:

VB = base area × height = 16 cm² × 3.5 cm = 56 cm³

Comparing the volumes, VA is approximately 103.67 cm³ and VB is 56 cm³. Therefore, the cone-shaped package of Brand A contains more seeds than the square prism package of Brand B.