Question

a pyramid has a volume of 563 cubic cm and a height of 37 cm. find the area of its base correct to the nearest cm².

Explanation:

Step1: Recall the volume formula for a pyramid

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

Step2: Rearrange the formula to solve for \( B \)

Starting with \( V = \frac{1}{3}Bh \), we can multiply both sides by 3 to get \( 3V=Bh \). Then, divide both sides by \( h \) to solve for \( B \), so \( B=\frac{3V}{h} \).

Step3: Substitute the given values into the formula

We know that \( V = 563 \) cubic cm and \( h = 37 \) cm. Substituting these values into the formula for \( B \), we get \( B=\frac{3\times563}{37} \).

Step4: Calculate the value of \( B \)

First, calculate the numerator: \( 3\times563 = 1689 \). Then, divide by 37: \( \frac{1689}{37}\approx45.6486 \). Rounding this to the nearest whole number (since we need the area correct to the nearest \( \text{cm}^2 \)), we get \( B\approx46 \).

Answer:

The area of the base of the pyramid is approximately \( \boldsymbol{46} \) square centimeters.