Answer:
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
