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Again maths problemmmm :(((( ?
1.)A solid sphere of diameter 42 cm is melted and recast into a number of smaller identical cones each of diameter 7 cm and height 3 cm. find the number of cones so formed.
2) find the equation of straight line which is passing through the point of intersection of the straight lines 2x+3y-1=0 and 3x+2y=4 and the midpoint of the straight line joining the two points (3/8,-7/10) and (-7/8,-3/10)
I got the first one answer as 1008 cones
1 Answer
- rosLv 59 years agoFavorite Answer
Sphere V = 4/3*pi*r^3
Cone V= 1/3*pi*r^2*h
Sphere
V = 4/3*pi*21^3
Number of cones = Vsphere/ V cone= (4/3*pi*21^3)/(1/3*pi*3.5^2*7)
= 432
2)
2x+3y-1=0..........(i)
3x+2y=4 ............(ii)
Multiply (i) by 3 and (ii) by 2
6x + 9y - 3 = 0..............(ia)
6x + 4y - 8 = 0.............(iia)
Subtract (iia) from (ia)
5y + 5 =0
y = -1
substituting y = -1 in (i)
2x+3y-1=0..........(i)
2x - 3 - 1 =0
2x = 4
x = 2
Point A (2,-1)
Midpoint of (3/8,-7/10) and (-7/8,-3/10)
= (x1 + x2)/2,(y1 + y2)/2
= (3/8 -7/8)/2, (-7/10 - 3/10)/2
Point B = (-1/4, -1/2)
y - y1 = ((y2 -y1)/(x2 -x1))*(x - x1)
y + 1 = ((-1/2 + 1)/(-1/4 - 2))*(x - 2)
y + 1 = -2/9*(x - 2)
9y + 9 = -2(x - 2)
9y + 2x + 13 = 0