Find the missing dimension for each three-dimensional figure to the nearest tenth, given the volume and other dimensions.
rectangular pyramid,
t=8m, w=4.6m, V=88m cubed
To find the missing dimension (height) of the rectangular pyramid, we can use the formula for the volume of a pyramid:
Volume = (1/3) x base area x height
Given:
t = 8m (length of the base)
w = 4.6m (width of the base)
V = 88m³ (volume)
First, let's calculate the base area using the given dimensions of the base:
Base area = t x w
Base area = 8m x 4.6m
Base area = 36.8m²
Now, rearrange the formula for volume to solve for the height:
Volume = (1/3) x base area x height
88m³ = (1/3) x 36.8m² x height
Next, isolate the height by multiplying both sides of the equation by 3 and dividing by the base area:
(1/3) x 36.8m² x height = 88m³
height = (88m³) / ((1/3) x 36.8m²)
height = (88m³) / (12.27m²)
height ≈ 7.18m
Therefore, the missing dimension (height) of the rectangular pyramid is approximately 7.18m.
To find the missing dimension for a rectangular pyramid, we can use the formula for the volume of a pyramid:
Volume = (1/3) * base area * height
In this case, the volume (V) is given as 88 cubic meters, and we have two dimensions, the base length (t) and base width (w).
First, we need to find the base area. The base area of a rectangular pyramid is given by:
Base Area = length * width
In this case, the base area is 8 meters * 4.6 meters = 36.8 square meters.
Now, let's substitute the values into the volume formula and solve for the missing dimension:
V = (1/3) * 36.8 * height
88 = (1/3) * 36.8 * height
To isolate the height, we can multiply both sides of the equation by 3:
3 * 88 = 36.8 * height
264 = 36.8 * height
Divide both sides of the equation by 36.8:
height = 264 / 36.8
height ≈ 7.17 meters
Therefore, the missing dimension (height) for the rectangular pyramid is approximately 7.17 meters.