## ammy1234 3 years ago Brenda made two similar glass display boxes shaped like triangular prisms. The length of the sides of the base of the first display box is 4 feet, and the length of the sides of the base of the second display box is 8 feet. If the volume of the first display box is 42 ft3, what is the volume of the second display box?

1. amistre64

4^2 sin(60) ---------- = base triangle area i believe 2

2. amistre64

|dw:1329592783061:dw| base = sqrt(3) sqrt(3) * h = 42 h = 42/sqrt(3) , is that right?

3. ammy1234

336 ft3 672 ft3 1344 ft3 2688 ft3

4. ammy1234

is the choices

5. amistre64

then with any luck we will arrive at one of those choices :)

6. ammy1234

ok lets do it

7. amistre64

|dw:1329592905817:dw| 4*4 sin(60) ---------- = base area 2 4*4*sqrt(3) --------- = 4sqrt(3) for the base area 4 4sqrt(3) * h = 42 h = 21/2sqrt(3)

8. amistre64

if we double this to be similar to the other one in measure we get a height of 21/sqrt(3)

9. amistre64

base area of other one is: 8*8 sin(60) 8*8*sqrt(3) ---------- = ---------- = 16 sqrt(3) 2 4 16sqrt(3) * 21/sqrt(3) = 16*21 ... 210 +126 = 336 ... maybe?

10. amistre64

yay!! its an option, if its right or not tho ... lol

11. ammy1234

good enough for me haha thanks

12. amistre64

yw, i cant see any fauxpauxes in my work so it might be good; at least an 83% chance of success lol