Final answer:
To find the base dimensions of a frustum of a square pyramid with a height of 6cm and a volume of 350cm^3, we use the volume formula of a frustum. After calculations, only option (d) Height: 6cm, Base side: 3cm satisfies the given conditions.
Option (d) .
Step-by-step explanation:
Finding the Base Dimensions of a Frustum
The question asks to determine the dimensions of the base of a frustum of a square pyramid with a height of 6cm and a volume of 350cm3, where one base area is four times the other.
To find the dimensions of the bases, we'll use the formula for the volume of a frustum of a pyramid: V = (1/3)h(A1 + A2 + √(A1A2)), where A1 and A2 are the areas of the two bases, and h is the height of the frustum.
Let the side of the smaller base be 's'. The area of the smaller base (A1) is s2, and the area of the larger base (A2) is 4s2. Plugging these values into the volume formula along with the given height and volume, we get:
350 = (1/3)*6(s2 + 4s2 + √(s2*4s2))
After solving for 's', we can find that the side length of the base of the frustum that matches the given volume is 3cm.
From the provided answer options, only option (d) corresponds to the side of the base with dimensions of Height: 6cm, Base side: 3cm, which matches the conditions of the problem.
Option (d)