Question

1. Devin is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 9 cm and the height of the pyramid is 10 cm. To get the wax for the candle, Devin melts cubes of wax that are each 4 cm by 4 cm by 4 cm. How many of the wax cubes will Devin need in order to make the candle? Show your work.

Answer 1

Answer:

The number of wax cubes required is 5.

Step-by-step explanation:

Devin is making a candle by pouring melted wax into a mold in the shape of a square pyramid.

Each side of the base of the pyramid is 9 cm and the height of the pyramid is 10 cm (as shown in figure below)

also, To get the wax for the candle, Devin melts cubes of wax that are each 4 cm by 4 cm by 4 cm

We have to find the number of wax cubes will Devin need in order to make the candle.

Consider Wax cubes of dimension 4 cm by 4 cm by 4 cm

Volume of cube =  (side)³

Thus, Volume of one wax cube is given by = (side)³

Volume of one wax cube  = (4)³= 64 cm³

Now we find the volume of square pyramid.

Volume of square pyramid = $\frac{1}{3} \cdot {\text{area of base}} \cdot \text{height}$

Thus, Volume of given square base with base side 9 cm and height 10 cm is

Area of square = (side)²

Volume of square pyramid = $\frac{1}{3} \cdot {9^2} \cdot 10$

Volume of square pyramid = $\frac{1}{3} \cdot {81} \cdot 10$

Volume of square pyramid = $270$

thus, the volume of square pyramid is 270 cm³

$\text{Number of cubes required}=\dfrac{\text{Volume of candle}}{\text{Volume of one wax cube}}$

$\text{Number of cubes required}=\frac{270}{64}$

$\text{Number of cubes required}=4.21$ (approx)

Thus, the number of wax cubes required is 4.21. Rounding it off to the nearest whole number, we will get 5.

Thus,the number of wax cubes required is 5.

Answer 2

(1/3)(9*9*10) = 270cm^3 for volume of pyramid

270/(4*4*4) = 4.22 cubes.

round up to 5 cubes