Question

13 multiple choice 2 points
find the volume of the square pyramid if the area of the base is 48 cm² and the height is 8 cm.
14 multiple choice 2 points
in which quadrilateral are the diagonals always perpendicular?

Explanation:

Step1: Recall the volume formula for a square pyramid

The volume formula for a square pyramid is \(V=\frac{1}{3}Bh\), where \(B\) is the area of the base and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(B = 48\mathrm{cm}^2\) and \(h=8\mathrm{cm}\), we substitute these values into the formula: \(V=\frac{1}{3}\times48\times8\).
First, calculate \(48\times8 = 384\). Then, \(\frac{1}{3}\times384=128\).

for Question 14:

• A trapezoid: Diagonals are not always perpendicular.
• A rectangle: Diagonals are equal in length but not always perpendicular.
• A square: It is a special case of a rhombus and a rectangle. In a square, the diagonals are equal in length, bisect each other, and are perpendicular.
• A parallelogram: Diagonals bisect each other but are not always perpendicular.

Answer:

\(128\mathrm{cm}^3\) (the third option)