Question

A triangular pyramid has a volume of 333 and one-third yards cubed. What are the possible measures of the area of the base, B, and the height, h, of the pyramid? (Recall the formula V = one-third B h.)
B = 50 centimeters squared; h = 10 centimeters
B = 50 centimeters squared; h = 30 centimeters
B = 100 centimeters squared; h = 10 centimeters
B = 100 centimeters squared; h = 30 centimeters

PLZ HELP ME

Answer 1

To find the option that satisfies the volume of the triangle, we can solve each option.

Formula for the volume a triangular prism: V = 1/3bh

Option A:

B = 50 centimeters squared; h = 10 centimeters

V = 1/3(50)(10)

V = 1/3(500)

V = 166.666... or 166 2/3 yards.

Therefore, this option is incorrect.

Option B:

B = 50 centimeters squared; h = 30 centimeters

V = 1/3(50)(30)

V = 1/3(1500)

V = 500 yards.

Therefore, this option is incorrect.

Option C:

B = 100 centimeters squared; h = 10 centimeters

V = 1/3(100)(10)

V = 1/3(1000)

V = 333.333... or 333 1/3 yards.

Therefore, this option is correct.

Option D:

B = 100 centimeters squared; h = 30 centimeters

V = 1/3(100)(30)

V = 1/3(3000)

V = 1000 yards.

Therefore, this option is incorrect.

Hence, the correct answer is [ B = 100 centimeters squared; h = 10 centimeters ]

Best of Luck!