A holiday ornament in the shape of a square pyramid has the following dimensions: 2.75 x 2.75 x 2.75 in. What is the approximate volume of the ornament? Round your answer to the nearest hundredth.(1 point)

Question

Responses

24.47 in.3
  24.47 in. cubed

6.93 in.3
6.93 in. cubed

9.01 in.3
  9.01 in. cubed

20.80 in.3
  20.80 in. cubed
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Answer 1

The volume \( V \) of a square pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times \text{base area} \times \text{height} \]

For a square pyramid, the base area is given by the area of the square base, which is the length of one side squared. Given that the dimensions are \( 2.75 , \text{in} \):

1. Calculate the base area: \[ \text{base area} = (2.75)^2 = 7.5625 , \text{in}^2 \]

2. Height of the pyramid (which is equal to the perpendicular height from the base to the apex of the pyramid, also given as 2.75 in): \[ \text{height} = 2.75 , \text{in} \]

3. Now compute the volume: \[ V = \frac{1}{3} \times 7.5625 \times 2.75 \] \[ V = \frac{1}{3} \times 20.803125 \] \[ V \approx 6.934375 , \text{in}^3 \]

Rounding to the nearest hundredth, the volume of the ornament is approximately: \[ \boxed{6.93} , \text{in}^3 \]