‘Find the volume of a pyramid with a square base, where the side length ofthe base is 13.9 cm and the height of the pyramid is 6.3 cm. Round your answer to the nearest tenth of a cubic centimeter: 3 cm Answer:’
The Correct Answer and Explanation is:
To find the volume of a pyramid with a square base, we use the formula:V=13×Base Area×HeightV = \frac{1}{3} \times \text{Base Area} \times \text{Height}V=31×Base Area×Height
Step 1: Find the base area.
Since the pyramid has a square base, the area of the base is simply the side length squared:Base Area=side length2=(13.9 cm)2=193.21 cm2\text{Base Area} = \text{side length}^2 = (13.9 \, \text{cm})^2 = 193.21 \, \text{cm}^2Base Area=side length2=(13.9cm)2=193.21cm2
Step 2: Apply the formula for the volume.
Now, substitute the values for the base area and height into the volume formula:V=13×193.21 cm2×6.3 cmV = \frac{1}{3} \times 193.21 \, \text{cm}^2 \times 6.3 \, \text{cm}V=31×193.21cm2×6.3cmV=13×1217.343 cm3V = \frac{1}{3} \times 1217.343 \, \text{cm}^3V=31×1217.343cm3V=405.78 cm3V = 405.78 \, \text{cm}^3V=405.78cm3
Step 3: Round to the nearest tenth.
The volume of the pyramid is approximately 405.8 cubic centimeters.
Explanation:
To determine the volume of any pyramid, we calculate the area of the base first. For a square base, this is the side length squared. Then, we use the formula V=13×Base Area×HeightV = \frac{1}{3} \times \text{Base Area} \times \text{Height}V=31×Base Area×Height to find the volume. The height is the perpendicular distance from the apex (top) of the pyramid to the base. The multiplication and division steps lead to the final volume, which is rounded to the nearest tenth, as requested. This formula is a general one, applicable to pyramids with square bases, triangular bases, or any other polygonal base.
