Volume formulas:
- Cube V = s³, (s - side),
- Cone V = πr²h/3, (r- radius, h- height),
- Sphere V = 4πr³/3, (r - radius)
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Volume of metal, is same as the volume of the cone with radius a and height 2a:
(i) The volume of the metal plank is half the volume of the metal:
- V = (1/2)(2πa³/3) = πa³/3
(ii) The volume of the two spheres is same as the volume of the plank, so the volume of each sphere is:
The volume of sphere with radius r is 3πr³/4, compare the two and solve for r:
- 3πr³/4 = πa³/6
- r³ = 4a³/18
- r³ = 2a³/9
- r = a∛(2/9)
(iii) Using the volume of the plank (cube), find the side length:
- V = s³ (s- side of cube)
- V = πa³/3
(iv)
Use the formula from the previous part and substitute values of a and π to get:
- a∛(π/3) =
- 12.5∛(3.14/3) =
- 12.5*1.01 =
- 12.6 (rounded)
