Jude says that the volume of a square pyramid with base edges of 12 in and a height of 10 in is equal to the volume of a cylinder with a radius of 6.77 in and a height of 10 in. Jude rounded his answers to the nearest whole numbers. Examine Jude's calculations. Is he correct?

Volume of Square Pyramid Volume of Cylinder

V = one third B (h) V = one thirdπr2h

V = one third (144) (10) V = one thirdπ (6.772) (10)

V = one third (1440) one thirdπ (45.8329) (10)

V = 480 in3 V = one thirdπ (458.329)

V ≈ 480 in3

Yes, his calculations are correct and the volumes for figures are equal.

No, he made a mistake in solving for the volume of the cylinder.

Yes, but he made a mistake in solving for the volume of the square pyramid.

No, he made a mistake in solving for the volume of both figures.

Question

Mathematics

Chad Booth

22 September, 06:35

Jude says that the volume of a square pyramid with base edges of 12 in and a height of 10 in is equal to the volume of a cylinder with a radius of 6.77 in and a height of 10 in. Jude rounded his answers to the nearest whole numbers. Examine Jude's calculations. Is he correct?

Volume of Square Pyramid Volume of Cylinder

V = one third B (h) V = one thirdπr2h

V = one third (144) (10) V = one thirdπ (6.772) (10)

V = one third (1440) one thirdπ (45.8329) (10)

V = 480 in3 V = one thirdπ (458.329)

V ≈ 480 in3

Yes, his calculations are correct and the volumes for figures are equal.

No, he made a mistake in solving for the volume of the cylinder.

Yes, but he made a mistake in solving for the volume of the square pyramid.

No, he made a mistake in solving for the volume of both figures.

+3

Answers (1)

Know the Answer?

Oscar Morrow · Answer 1

No, not correct

Step-by-step explanation:

Square pyramid volume: (1/3) (base area) (height). In this case,

V = (1/3) * (12 in) ^2 * (10 in) = 480 in^3 = 480 in^3

Cylinder volume: (base area) * (height). In this case,

V = (3.14) * (6.77 in) ^2 * (10 in) = 452.12 in^3.

No, Jude is not correct; the 480 in^3 volume of the square pyramid is not the same as the 452.12 in^3 volume of the cylinder.