find the volume of the coposite figrue tot he nearest whole number
A rectangular prism has a height of 6mm, depth of 11mm and width of 9mm. A half cylinder is shown on top of the rectangular prism.
To find the volume of the composite figure, we need to calculate the volume of the rectangular prism and the half cylinder separately and then add them together.
Volume of rectangular prism = height × depth × width
= 6 mm × 11 mm × 9 mm
= 594 cubic mm
For the half cylinder, we first need to calculate the volume of a full cylinder and then divide by 2.
Volume of a full cylinder = π × r^2 × h
Here, the radius (r) and height (h) of the cylinder are the width and height of the rectangular prism, respectively.
r = 9mm / 2 = 4.5 mm
h = 6 mm
Volume of full cylinder = π × (4.5 mm)^2 × 6 mm
≈ 3.14 × 20.25 × 6
≈ 381.51 cubic mm
Now we need to find the volume of the half cylinder.
Volume of half cylinder = Volume of full cylinder / 2
≈ 381.51 / 2
≈ 190.76 cubic mm
Now, we can find the volume of the composite figure by adding the volumes of the rectangular prism and half cylinder.
Volume of composite figure ≈ 594 + 190.76
≈ 784.76 cubic mm
Since we need to find the volume to the nearest whole number, rounding it off gives us:
Volume of composite figure ≈ 785 cubic mm