# Write an equation that can be used to determine the length, x, in inches of each piece of yarn that

###### Question:

## Answers

a) 22 pine trees

b) x² = 2² + 0.75²

Step-by-step explanation:

a) The volume of a cube is given as:

Volume of cube = length³

The length of the cube = length of the edges = 3 inches, hence:

Volume of cube = (3 inches)³ = 27 in³

The pine tree is the shape of a cone with diameter of 1.5 inches and a height (h) of 2 inches. The radius (r) = diameter / 2 = 1.5 inches / 2 = 0.75 inches.

The volume of the cone = πr²(h/3) = π × (0.75)² × (2/3) = 1.178 in³

The number of pine trees that the artist can make = Volume of cube / Volume of cone = 27 / 1.178 = 22.9

The number of pine trees that can be made = 22

b) The yam length need to extend from the top of the tree to the base is the same as the slant height of the cone.

Let the yam length be x, therefore:

x² = height² + radius²

x² = 2² + 0.75²

x² = 4 + 0.5625 = 4.5625

x = √4.5625 = 2.136 in

The yam length is 2,136 in