- If x varies as y and if x = 6 when y = 3, find x when y = 10.
Solution:
Given x varies as y and if x = 6 we have y = 3
x α y
x=6 y=3
x=? y=10
x=ky
6=k.3 ⇒k = 2
x = 2 x y = 2 x 10 = 20
- If p varies as q and if p = 5 when q = 10, find when p = 20.
Solution:
Given p varies as q and if p = 5 when q = 10
p = kq
5 = kx10
k = 5/10 = 1/2
If p = 20 then q=?
p = kq
20 = 1/2 x q
q = 20 x 2 = 40
- If y varies directly as √x and y = 24 when x = 3, find y when x = 16
Solution:
Given y varies directly as √x and y = 24 when x = 3
Such that, y = k√x
24 = k√3
k = 24/√3 = 24/√3 x √3/√3 = 24x√3/3 = 8√3
If x = 16 then y = ?
y=k√x
y = 8√3 x √16 = 8√3×4 = 32√3
- Given that the volume of a sphere varies as the cube of its radius and its volume is 179.7 cm3 when radius is 3.5, find the volume when radius is 1.75 cm
Solution:
Given, the volume of a sphere varies as the cube of its radius.
Volume of sphere = (radius)3
Volume=179.7cm3 Radius=3.5 cm
Volume=? radius=1.75cm
volume of sphere α r3
volume = k. (radius)3
179.7 = k(3.5)3
k = 179.7/3.5×3.5×3.5 = 1797/3.5×3.5x.3.5 = 1797/428.75 = 4.1912
k = 4.1912
volume = k. (radius)3
=4.1912 x (1.75)3
= 22.46cm3
- The distance through which a body falls from rest varies as square of time it takes to fall that distance. It is known that the body falls 64 cm in 2 seconds. How far does that body fall in 6 seconds?
Solution:
h1 α t2
h = 64cm t = 2sec
h = ? t = 6 sec
h1 α t2
h1 =k. t2
64 = k. (2)2
k = 64/4 = 16
If t = 6sec.
h1 =k. t2
h1 = 16 x 62
= 16 x 36 = 576 cm
- the area of an isosceles: right angled triangle varies directly as the square of the length of its leg. If the area is 18 cm2 when the angle of its leg is 6 cm, find (i) the relation between area and length
(ii) area of triangle when length of its leg is 5 cm.
Solution:
A of triangle α b2
A = 18 cm2
b = 6 cm.
(i) the relation between area and length
A of triangle α b2
A = kb2
18 = k.62
k = 18/36 = 1/2
(ii) area of triangle when length of its leg is 5 cm.
A = kb2
A = 1/2 x (5)2 = 25/2 = 12.5 cm2
1 thought on “Variation – Exercise 3.6.2 – Class IX”
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