Question

HELP WITH 2 MATH QUESTIONS!!

1) Sarah is making a candle by pouring melted wax into a mold in the shape of a cylinder. The diameter of the cylinder mold is 6 and the height of the cylinder is 8 cm. To get the wax for the candle, Sarah melts cubes of wax that are each 3 cm by 3 cm by 3 cm. How many of the wax cubes will Sarah need in order to make the candle? Show your work.

2) Jim is making fish tanks out of 2 rectangular prisms. He will use triangle ABC for the base of one prism and triangle DEF for the base of the other prism.
A) is ABC similar to DEF? Explain.
B) Suppose he makes both prisms with the same height and fills them both with water. Which prism will have a greater volume? How many times great? Show your work.
I’m a bit lost. Please help!

Answer 1

Explanation:

In order to determine the number of wax cubes needed to make the candle, we divide the volume of the pyramid by the volume of the cube. That is,

number of wax = volume of mold / volume of wax

The formulas are,

number of wax = (1/3)Ah / s³

Where A is the area of the base, in this case 9 cm x 9 cm which is equal to 81 cm². Substituting the known values from the given above,

number of wax = (1/3)(81 cm²)(10 cm) / (4 cm)³ = 4.21

Thus, approximate number of wax should be 4.21. If we are to round this off to the nearest whole number, we will get 5 (considering that we want rather to have excess than missing items)

Answer 2

9 cubes.

Explanation:

The volume of the mould = π r^2 h

= π *3^2 * 8

= 72π cm^3

Area of 1 cube = 3^3 = 27 cm^3

So the number of cubes required to fill the mould

= 8.38 cubes.

So it will need 9 cubes.

2.

The CORRESPONDING sides are in the same ratio so the 2 triangles are similar:

6/9 = 2/3

AND

8/12 = 2/3.

B.

Suppose he makes both prisms = 10 cms high.

The volume of the larger prism = 1/2 * 12 *9 * 10 = 540 and the volume of the smaller prism = 1/2 * 6 * 8 * 10 = 240.

So it is 540 / 240 = 2.25 times greater.