Question

2. The height of one square pyramid is 24 m. A similar pyramid has a height of 8 m. The volume of the larger pyramid is 648 m3. The surface area of the smaller pyramid is 124 m^2. Determine each of the following, showing all your work and reasoning:
a.) Find the scale factor that would take your from the small pyramid to the bigger one. (4 points)

b.) What is the surface area of the larger pyramid? (4 points)

c.) Volume of the smaller pyramid (4 points)

d.) Ratio of the volume of the smaller pyramid to the larger pyramid (4 points)

Answer 1

Larger PyramidHeight 24 Volume 648

Pyramid Volume = (Area of the Base * Height) ÷ 3648 = Base Area * 24 / 3Base Area = 648 * 3 / 24Base Area = 648 / 8Base Area = 81Base Length = 9
a) The Scale Factor between the Small & Large PyramidLength - 3LATERAL Area - 9Volume - 27

Slant Height^2 = 4.5^2 + 24^2Slant Height^2 = 596.25 Slant Height^2 = 24.4182308941
b)
Large Pyramid Area = (½ * Perimeter of Base * Slant Height) + Base AreaLarge Pyramid Area = (.5 * 36 * 24.4182308941) + 81
Large Pyramid Area = 439.5281560938 + 81
Large Pyramid TOTAL Area = 520.5281560938 Large Pyramid LATERAL Area = 439.5281560938


**********************************************************************************c)
Smaller PyramidHeight 8Surface Area = 124
This pyramid has dimensions that are one third of the larger pyramid.Therefore, it has a base length of 3.Base Area = 9.
Its base perimeter would be 12.
Small Pyramid Volume = (Area of the Base * Height) ÷ 3Small Pyramid Volume = ( 9 * 8 ) / 3Small Pyramid Volume = 72 / 3
c) Small Pyramid Volume =24 cubic meters

d) Ratio of larger pyramid volume to smaller pyramid volume648 / 24 = 27The reason? Volume is a 3 dimensional quantity.  The Larger pyramid is 3 times larger in terms of the base measurement.9 meters vs 3 meters - a factor of 3When we compare volumes, we have to cube this factor.3^3 = 27

Source : http://www.1728.org/volpyrmd.htm