Volume and Surface Area of Solid Figures
- A cone has height which is half of 16.8 cm, while diameter of its base is 4.2 cm. It is melted and recast into a sphere. Find the surface area of the sphere. ?
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Given that, Height = 1 m
Diameter = 140 cm or 140/100 m = 1.40 m
∴ r = 1.40/2 = 0.7 m
Now,
Required sheet = Total surface area = 2πr( h + r)Correct Option: A
Given that, Height = 1 m
Diameter = 140 cm or 140/100 m = 1.40 m
∴ r = 1.40/2 = 0.7 m
Now,
Required sheet = Total surface area = 2πr( h + r)
= (22/7) x 1.4 x (1 + 0.7) = 7.48 sq m
∴ Sheet required = 7.48 sq m
- A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the top most ball touches the upper cover of the box, then volume of the empty space in the box is ?
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Height of the cylinder = 10 x Diameter of each ball
= 10 x 10 = 100 cm
∴ Required empty space
= π (5)2 (100) - 4/3 π (5)3 x 10Correct Option: A
Height of the cylinder = 10 x Diameter of each ball
= 10 x 10 = 100 cm
∴ Required empty space
= π (5)2 (100) - 4/3 π (5)3 x 10
= π (5)2 x 10 [10 - 20/3]
= π (5)2 x 10 [30 - 20/3] = 2500/3 π cm3
