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The night of one square pyramid is 24m. A similar pyramid has a height of 8m. The volume of the larger pyramid is 648 m^3. 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

B) what is the surface area of the larger pyramid

C) volume of the smaller pyramid

D) ratio of the volume of the smaller pyramid to the larger pyramid

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znk znk · Answer 1 · 2019-04-17T23:32:37+02:00

Answer:

A) 3; B) 1116 m²; C) 24 m³; D) 1/27

Step-by-step explanation:

A) Scale factor

The scale factor is the ratio of the heights of the two pyramids.

h₂/h₁ = 24/8 = 3

B) Surface area

The ratio of the surface areas is the square of the scale factor.

A₂/A₁ = 3²

A₂/124 = 9

A₂ = 124 × 9 = 1116 m²

The volume of the larger pyramid is 1116 m².

C) Volume

The ratio of the volumes is the cube of the scale factor.

V₂/V₁ = 3³

648/V₁ = 27

648 = 27V₁

V₁ = 648/27 = 24 m³

The volume of the smaller pyramid is 24 m³.

D) Volume ratio

V₁/V₂ = 24/648 = 1/27

The volume ratio is 1/27.