Question

MARK AS BRAINLIEST An artist has a block of clay in the shape of a cube. The edges of the cube measure 3 inches. The artist will use the clay to make models of
pine trees. Each tree will be a solid cone with a base diameter of 1.5 inches and a height of 2 inches.
Part A
Determine the greatest number of clay pine trees that the artist can make. Show your work.

Answer 1

Answer:

22

Step-by-step explanation:

The volume of a cube is given as:

Cube volume = length × length × length

Since the edges of the cube measure 3 inches, this means that the length of the cube is 3 inches, therefore:

Cube volume = 3 inches × 3 inches × 3 inches = 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 can be made = Volume of cube / Volume of cone = 27 / 1.178 = 22.9

The number of pine trees = 22