Question

Tower one, a cube with a hexagonal prism measures 15.6cm. Tower two, a cube with a cylinder measures 18.3cm. Tower 3, a hexagonal prism with a cylinder measures 13.9cm. What is the height of the 4th tower when all three shapes are used?

Answer 1

`Tower 4 = 23.9cm`

Explanation:

Given

Tower one = 15.6 cm

Tower two = 18.3 cm

Tower 3 = 13.9 cm.

Required:

Height of the 4th tower

Represent a cube by X; a cylinder by Y and a hexagonal prism by Z

Tower one, a cube with a hexagonal prism = X + Z = 15.6

Tower two, a cube with a cylinder = X + Y = 18.3

Tower 3, a hexagonal prism with a cylinder = Z + Y = 13.9

`X + Z = 15.6` ----- Equation 1

`X + Y = 18.3` ----- Equation 2

`Z + Y = 13.9` ----- Equation 3

Subtract equation 1 from 2

`(X + Y = 18.3) - (X + Z = 15.6)`

`X - X + Y - Z = 18.3 -15.6`

`Y - Z = 18.3 -15.6`

`Y - Z = 2.7` ---- Equation 4

Add Equation 4 to Equation 3

`(Y - Z = 2.7) + (Z + Y = 13.9)`

`Y + Y - Z + Z = 2.7+ 13.9`

`2Y = 2.7+ 13.9`

`2Y = 16.6`

Divide both sides by 2

`(2Y)/(2) = (16.6)/(2)`

`Y = (16.6)/(2)`

`Y = 8.3cm`

Substitute
`Y = 8.3cm` in Equation 2 and 3

`X + Y = 18.3` ----- Equation 2

`X + 8.3 = 18.3`

Subtract 8.3 from both sides

`X + 8.3 - 8.3 = 18.3 - 8.3`

`X = 18.3 - 8.3`

`X = 10cm`

`Z + Y = 13.9` ----- Equation 3

`Z + 8.3 = 13.9`

Subtract 8.3 from both sides

`Z + 8.3 - 8.3 = 13.9 - 8.3`

`Z = 13.9 - 8.3`

`Z = 5.6cm`

So, we have that

`X = 10cm`

`Y = 8.3cm`

`Z = 5.6cm`

The question states that the 4th tower is made up of the three shapes;

This implies that;

`Tower 4 = X + Y + Z`

`Tower 4 = 10cm + 8.3cm + 5.6cm`

`Tower 4 = 23.9cm`

The height of the 4th tower is 23.9cm