Question

I need to know this quick

Answer 1

1. Volume of the composite figure is 943.89 mm³

2. The volume, of the is 144 cm³

Explanation:

1. The composite figure comprises of a cube and a half cylinder;

Volume of a cube = 9 mm × 11 mm × 6 mm = 594 mm³

Volume of the half cylinder = area of base × length = (π·r²)/2 × l

Where:

r = (Diameter of base)/2 = 9/2 = 4.5 mm

l = 11 mm

Therefore, plugging the values, gives;

Volume of the half cylinder = (π × 4.5²)/2 × 11 = 349.89 mm³

Hence, volume of the composite figure = Volume of the cube + Volume of the half cylinder

Volume of the composite figure = 594 mm³ + 349.89 mm³ = 943.89 mm³

2. The volume, V of a pyramid is given by the following relation;

`V = (l * w * h)/(3)`

Where:

l = Length of base = 8 cm

w = Width of the base = 6 cm

h = Height of the pyramid = 9 cm

`V = (8 * 6 * 9)/(3) = 144 \ cm^3`

Here we have that a cube of side x, therefore, the area = x·x, integrating we have;

`\int\limits^x_0 {x \cdot x} \, dx = (x^3)/(3)`

Where:

Length, height width of the pyramid = x

It can therefore be shown, that for a pyramid of length, l, width, w, and height, h, the volume,
`V = (l * w * h)/(3)` .

Answer 2

1) 943.895 mm3

2) 144 cm3

Explanation:

1)

First we need to find the volume of the rectangular prism:

Volume_1 = 9 * 11 * 6 = 594 mm3

Then, we can find the volume of the half cylinder above the prism:

Volume_2 = 0.5*(pi * (4.5^2) * 11) = 349.895 mm3

So the volume of the figure is the sum of both volumes:

Volume_total = Volume_1 + Volume_2 = 943.895 mm3

2)

The volume of a pyramid is one third of the base area multiplied by the height, so we have:

Volume = (1/3) * 6 * 8 * 9 = 144 cm3