Question

2. Similar pyramids have heights 12 cm and 20 cm. The volume of the larger pyramid is 8192 cm3. Determine each of the following, showing all your work and reasoning.
(a) The scale factor of the smaller pyramid to the larger pyramid in simplest form
(b) The ratio of the area of the base of the smaller pyramid to the base of the larger pyramid
(c) Ratio of the volume of the smaller pyramid to the larger
(d) The volume of the smaller pyramid

Answer 1

We know that

[volume of a pyramid]=[area of the base]*h/3

a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

12/20----------> 3/5
the answer Part a) is 3/5

(b) The ratio of the area of the base of the smaller pyramid to the base of the larger pyramid

[The ratio of the area of the base of the smaller pyramid to the base of the larger pyramid]--------> (3/5)²------> 9/25------> 0.36

[volume of a larger pyramid]=8192 cm³
h=20 cm
so
[8192]=[area of the base larger pyramid]*20/3
[area of the base larger pyramid]=8192*3/20------> 1228.80 cm²

[area of the base smaller pyramid]=(3/5)²*1228.80-----> 442.37 cm²

The ratio of the area of the base of the smaller pyramid to the base of the larger pyramid-----------> 442.37/1228.8--------> 0.36
0.36--------> is equal to (3/5)²

the answer part b) is 0.36  

(c) Ratio of the volume of the smaller pyramid to the larger

[Ratio of the volume of the smaller pyramid to the larger]=(3/5)³---> 27/125
27/125------> 0.216

the answer Part c) is 0.216

(d) The volume of the smaller pyramid

[The volume of the smaller pyramid]=0.216*8192------> 1769.47 cm³

the answer part c) is 1769.47 cm³