genuity Quiz
Find the height of a right square pyramid that has a rectangular
pase area of 70 square units and a volume
of 140 cubic units.
OA) 2 units
O B) 6 units
OC) 1 units
OD) 18 units



Answer :

To find the height of a pyramid, we can use the formula for the volume of a pyramid, which is: \[ V = \frac{1}{3} \times \text{base area} \times \text{height} \] Where: - \( V \) is the volume of the pyramid. - The base area is the area of the base of the pyramid. - The height (\( h \)) is the perpendicular distance from the base to the apex. We are given the following values: - The base area is 70 square units. - The volume (\( V \)) is 140 cubic units. Let's plug these values into the formula and solve for the height (\( h \)): \[ 140 = \frac{1}{3} \times 70 \times h \] To isolate \( h \), we multiply both sides of the equation by 3 and divide by the base area: \[ h = \frac{3 \times 140}{70} \] Now we simplify the right side of the equation: \[ h = \frac{3 \times 140}{70} = \frac{420}{70} \] \[ h = 6 \] Therefore, the height of the pyramid is 6 units. The correct answer is B) 6 units.