1.Use the figure to answer the questions.

(a) Explain why the triangles are similar.

(b) Find the value of y. Show your work

2. Danae is making a candle by pouring melted wax into a mold in the shape of a cone. The radius of the base of the cone is 2 in and the height of the cone is 8 in. To get the wax for the candle, Danae melts blocks of wax that are each 1 in by 1 in by 2 in. How many of the wax cubes will Danae need in order to make the candle? Show your work.

StrongJet
Jun 16, 2017

#1**+2 **

1.

(a)

Since ∠C = ∠S , these triangles are similar IF

\(\frac{30}{45}=\frac{16}{24} \\~\\ \frac{30\,\div\,15}{45\,\div\,15}=\frac{16\,\div\,8}{24\,\div\,8} \\~\\ \frac23=\frac23\qquad\text{true}\)

So, these triangles are similar.

(b)

Since these triangles are similar...

\(\frac{y}{14}=\frac{30}{16} \\~\\ y=\frac{30}{16}\,*\,14 \\~\\ y=26.25\)

2.

volume of cone = (1/3) * (pi * radius^{2}) * (height)

= (1/3) * (pi * 2^{2}) * (8)

= (1/3) * pi * 4 * 8

= 32pi / 3 cubic inches

volume of block = length * width * height

= 1 * 1 * 2

= 2 cubic inches

How many blocks fit into the cone?

How many 2 cubic inches fit into 32pi / 3 cubic inches ?

\(\frac{32\pi}{3}\,\div\,2 \,=\,\frac{32\pi}{3}\,*\,\frac12\,=\,\frac{32\pi}{6}\,\approx\,16.755\)

hectictar
Jun 16, 2017