4. If the perimeter and area of a circle are numerically equal. Find
its radius.
5. Find the area of a sector of a circle with radius 6cm and angle at
center is 60°
6. A solid piece of iron in the form of a cuboid of dimension
49cmx33cm x 24cm is melted to form a solid sphere. Find the
radius of sphere.
7. An underground water tank is in the form of a cuboid of edges
48m, 36mand 28m. Find the volume of the tank.
8. The diameter of the base of a right circular cylinder is 28 cm
and its height is 21cm. Find its curved surface area.
9. The surface area of two spheres are in the ratio 16:9.The ratio
of their volume is ------
10. A cylinder, a cone and a hemisphere have same base and
same height. Find the ratio of their volumes.
Answers
Step-by-step explanation:
4) perimeter = area
2πr = πr^2
2= πr^2/πr
2 = r
therefore, the radius is 2 units
5) area of sector = theta / 360° × πr^2 = 60/360×22/7×6×6 = 132/7 cm^2
6) volume of cuboid = volume of sphere
l×b×h = 4/3πr^3
49×33×24 = 4/3×22/7×r^3
38808 = 88/21 × r^3
3√9261 = r
21 cm = r
therefore the radius = 21 cm
7) volume of tank = l×b×h = 48×36×28 = 13824 m^3
8) csa of cylinder = 2πrh = 2×22/7×14×21 = 2×22×2×21 = 1848 cm^2
9) let radii of both the sphere be r1 and r2.
surface area of both the spheres = 4πr1^2 and 4πr2^2
ATQ...
r1^2:r2^2
16:9
=> r1^2/r2^2 = (4/3)^2 = 4:3
=> (r1/r2)^3 = (4/3)^3 = 64/27
therefore, the ratio of their volumes = 64:27
10) let the base radii of them be r and height be h.
then ratio of their volumes
cone: hemisphere: cylinder
1/3πr^3h : 2/3πr^3 : πr^2h ( but h = r)
1/3πr^2 r : 2/3πr^3 : πr^2 r
1/3πr^3 : 2/3πr^3 : πr^3
1/3 : 2/3 : 1
1:2:3
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