V=(s^(2)h)/(3) The formula gives the volume of a right square pyramid of height h and square base of side length s. If the side length of a right square pyramid increases by 30% while the height remains constant, what happens to the volume? Choose 1 answer: (A) The volume increases by 30%. (B) The volume increases by 69%. (C) The volume increases by 169%. (D) The volume increases by 300%.

Question

V=(s^(2)h)/(3) The formula gives the volume of a right square pyramid of height  h and square base of side length  s. If the side length of a right square pyramid increases by  30% while the height remains constant, what happens to the volume? Choose 1 answer: (A) The volume increases by  30%. (B) The volume increases by  69%. (C) The volume increases by  169%. (D) The volume increases by  300%.

Bytelearn · Accepted Answer

Denoting original side length: Let's denote the original side length of the square base as s and the height of the pyramid as h. The original volume V of the pyramid is given by the formula V = (s^2 * h) / 3. Now, if the side length increases by 30%, the new side length s' will be s' = s + 0.30s = 1.30s. We need to calculate the new volume V' with the increased side length and compare it to the original volume V to find the percentage increase.Calculating new side length: Using the formula for the volume of the pyramid with the new side length s', the new volume V' is V' = ((1.30s)^2 * h) / 3. We need to square the new side length (1.30s)^2 to find the factor by which the volume increases.Calculating new volume: Calculating the square of the new side length gives us (1.30s)^2 = (1.30)^2 * s^2 = 1.69 * s^2. This shows that the area of the base, and thus the volume, increases by a factor of 1.69 when the side length increases by 30%.Expressing new volume in terms of original volume: Now we can express the new volume V' in terms of the original volume V. Since V = (s^2 * h) / 3, the new volume V' will be V' = (1.69 * s^2 * h) / 3 = 1.69V. This means the new volume is 1.69 times the original volume.Calculating percentage increase in volume: To find the percentage increase in volume, we subtract the original volume from the new volume and then divide by the original volume: Percentage increase = ((V' - V) / V) * 100%. Substituting V' = 1.69V and V, we get Percentage increase = ((1.69V - V) / V) * 100% = (0.69V / V) * 100% = 69%.Conclusion: Therefore, the volume of the pyramid increases by 69% when the side length increases by 30% while the height remains constant. This corresponds to answer choice (B).

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