Let N cones be needed
Then, 1/3 ?r2 h x N = ?r2h
? N = 3
? 4/3 x 22/7 x r3 = 38808
? r3 = (38808 x 7/22 x 3/4)
= (21)3
? r = 21 cm
So, curved surface area of sphere
= 4?r2
= (4 x 22/7 x 21x21) cm2
= 5544 cm2
Let breadth = L meters. Then, height = 5L meters and length = 40L meters
? L x 5L x 40L = 12.8
? L3 = 12.8/200 = 128/2000 = 64/1000
? L = 4/10
Thus, breadth = (4/10) m = (4 x 100)/10 cm = 40 cm
Let original radius = r and original length = h
New radius = r/3
Let new length = H
Then, ? r2h = ? (r/3)2 x H = ? r2H/9
? H = 9h
Thus, the length becomes 9 times .
Volume of cube formed = 216 cm3
? Edge of the cube = (6 x 6 x 6)1/3 = 6 cm
Surface area of original metal sheet = 2(27 x 8 + 8 x 1 + 27 x 1) cm2 = 502 cm2
Surface area of the cube formed = [6 x (6)2] cm2 = 216 cm2
? Required difference in area of two solids = (502 - 216) cm2
= 286 cm2
Number of bricks required = Volume of wall in cm3 / Volume of 1 brick
= (200 x 100 x 1.8 x 100 x 37.5)/(25 x 12.5 x 7.5)
= 57, 600
? Required cost = Rs. (750 x 57600)/1000
= Rs. 43, 200
Let the height of cylinder = h
and height cone = H
Then, ?r2 h = 1/3 ?r2 H
? h/H = 1/3 = 1 : 3
? ? x (4)2 x h = 4/3 ? x (3)3
? h = 9/4 cm
= 2.25 cm
? 4/3 ?r3 = ?r2 h
? h = 4/3 r
? Height = 4/3 times its radius.
? Circumference of the girth = 440 cm
? 2?r = 440
? r = 440 / (2 x 7/22) = 70 cm
Thus, Outer radius = 70 cm
Inner radius = (70 - 4) cm = 66 cm
Volume of iron = ?[(70)2 - (66)2] x 63 cm3
= (22/7) x 136 x 4 x 63 cm3
= 107712 cm 3
Let the number of spheres be N
Then, N x 4/3 ? x (3)3 = ? x (2)2 x 45
? 36N = 180
? N = 180/36 = 5
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