+0

0
144
1
+4

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
Sort:

#1
+5243
+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 * radius2) * (height)

=  (1/3) * (pi * 22) * (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

### 20 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details