Joel built a model town. He constructed three buildings that each had a volume of 18 cm cubed. Each building looked different. What might Joe's buildings have looked like?

The three buildings can look like following:

1. The building can look like a cube, with each side and height equal to 2.62 cm.

2. The building can look like a cuboid, with 3 cm length, 1 cm breadth and 6 cm height.

3. The building can look like a pyramid, with 3 cm length, 3 cm breadth and 6 cm height.

Step-by-step explanation:

The three possibilities of the appearance or shape of the building, with the volume equal to 18 cm³ are as follows:

1. CUBIC SHAPE:

The building can look like a cube with the length of each side and height given as:

Volume of Cube = 18 cm³ = L³

L = ∛18 cm³ = 2.62 cm

Thus, the building can look like a cube, with each side and height equal to 2.62 cm.

2. CUBOID SHAPE:

The building can also look like cuboid with the following dimensions.

Length = 3 cm

Breadth = 1 cm

Height = 6 cm

Thus, the volume becomes:

Volume of Cuboid = Length * Breadth * Height

Volume of Cuboid = 3 cm * 1 cm * 6 cm = 18 cm³

Thus, the building can look like a cuboid, with 3 cm length, 1 cm breadth and 6 cm height.

3. PYRAMID SHAPE:

The building can also look like pyramid with the following dimensions.

Length = 3 cm

Breadth = 3 cm

Height = 6 cm

Thus, the volume becomes:

Volume of Pyramid = (Length * Breadth * Height)/3

Volume of Cuboid = (3 cm * 3 cm * 6 cm)/3 = 18 cm³

Thus, the building can look like a pyramid, with 3 cm length, 3 cm breadth and 6 cm height.

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solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.