BRAINLIEST An artist has a book 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 8
The artist plans to decorate each clay pine tree with pieces of yam that will extend directly from the top of the tree to the base of the tree.
write an equation that can be used to determine the length, x, in inches, of each piece of yam that the artist will need. Explain your
equation

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

76%

step-by-step explanation:

24% are dogs and the remaining is 76% because 100-24=76

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.