Jane builds a ramp made of a triangular prism and a rectangular prism. What is the volume of the ramp? 28 m3 1 m 7.5 m3 4 m 11.5 m3 2 m 3.5 m 15 m3
To find the volume of the ramp, we need to calculate the volume of each prism separately and then add them together.
The volume of a triangular prism is given by the formula V = (1/2) * b * h * l, where b is the base length, h is the height, and l is the length.
In this case, the base of the triangular prism is 1 m, the height is 7.5 m, and the length of the ramp is 4 m. So the volume of the triangular prism is V1 = (1/2) * 1 * 7.5 * 4 = 15 m^3.
The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.
In this case, the length of the rectangular prism is also 4 m, the width is 1 m, and the height is 11.5 m. So the volume of the rectangular prism is V2 = 4 * 1 * 11.5 = 46 m^3.
Therefore, the volume of the ramp is V1 + V2 = 15 + 46 = 61 m^3.
So the volume of the ramp is 61 m^3.
To find the volume of the ramp, we need to calculate the volume of the triangular prism and the rectangular prism separately, and then add them together.
Let's start with the triangular prism:
The formula to calculate the volume of a triangular prism is:
Volume = (1/2) * base * height * length
Given that the base of the triangular prism is 1 m and the height is 7.5 m, let's substitute these values into the formula:
Volume of triangular prism = (1/2) * 1 m * 7.5 m * length
Now let's move to the rectangular prism:
The formula to calculate the volume of a rectangular prism is:
Volume = length * width * height
Given that the length is 4 m, the width is 2 m, and the height is 3.5 m, let's substitute these values into the formula:
Volume of rectangular prism = 4 m * 2 m * 3.5 m
Now let's calculate the volumes and add them together:
Volume of triangular prism = (1/2) * 1 m * 7.5 m * length = 3.75 m^2 * length
Volume of rectangular prism = 4 m * 2 m * 3.5 m = 28 m^3
Total volume of the ramp = Volume of triangular prism + Volume of rectangular prism = 3.75 m^2 * length + 28 m^3
Since we don't have the length of the ramp, we don't have enough information to calculate the total volume.
To find the volume of the ramp made of a triangular prism and a rectangular prism, we need to calculate the volumes of each shape and then sum them up.
First, let's find the volume of the triangular prism. The formula for the volume of a triangular prism is V = (1/2) * base * height * length. From the given options, we have the following information for the triangular prism:
Base = 4 m
Height = 2 m
Length = 7.5 m
Using the formula, we can calculate the volume of the triangular prism:
V_triangular_prism = (1/2) * 4 m * 2 m * 7.5 m
= 4 m * 2 m * 7.5 m
= 60 m^3
Now, let's find the volume of the rectangular prism. The formula for the volume of a rectangular prism is V = length * width * height. From the given options, we have the following information for the rectangular prism:
Length = 1 m
Width = 3.5 m
Height = 15 m
Using the formula, we can calculate the volume of the rectangular prism:
V_rectangular_prism = 1 m * 3.5 m * 15 m
= 52.5 m^3
Finally, we can find the total volume of the ramp by summing up the volumes of the triangular prism and the rectangular prism:
Total volume = V_triangular_prism + V_rectangular_prism
= 60 m^3 + 52.5 m^3
= 112.5 m^3
So, the volume of the ramp is 112.5 m^3. None of the given options matches this answer, so it seems there may be an error in the provided choices.