30 POINTS

shane has two similar regular pyramids with pentagon shaped bases. the smaller has a scale factor of 2:3 when compared to the larger. only the small pyramid is shown.
he calculates the area of the base of the pyramid (through long, hard work) to be 110.11 square units. the height of the pyramid is 12 units. he now needs to calculate the volume of the pyramid.

A. calculate the volume of the pyramid for shane.

B. "oh no!" shane exclaims. "now i have to go through all this hard work again to find the volume of the larger pyramid!" does he? explain:

C. calculate the volume of the larger pyramid for shane.

A) 440.44 units³

B) similar figures

C) 1486.485 units³

Step-by-step explanation:

Volume = ⅓× base area × height

= ⅓ × 110.11 × 12 = 440.44 units³

B) he doesn't have to make calculations again because the two pyramids are similar.

If the ratio of sides is given, he can find the other volume using:

(side1/side2)³ = volume1/volume2

(2/3)³ = 440.44/volume2

Volume2 = 440.44 × 27/8

Volume2 = 1486.485 units³

Step-by-step explanation:

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet