. Which of the following conditions should be given to make the total surface area of a sphere and cylinder to be equal? (1) Diameter of a sphere should be equal to the radius of a cylinder. (2) Radius and height of a cylinder is equal to the radius of a sphere. (3) Radius of a cylinder should be double the radius of sphere. (4) Height of a cylinder should be equal to the diameter of the sphere.
Answers
Answer:
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Answer:
Q.1. Two cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Sol. Volume of each cube = 64 cm3
∴ Total volume of the two cubes = 2 × 64 cm3
= 128 cm3
Let the edge of each cube = x
∴ x3 = 64 = 43
∴ x = 4 cm
Now, Length of the resulting cuboid l = 2x cm
Breadth of the resulting cuboid b = x cm
Height of the resulting cuboid h = x cm
∴ Surface area of the cuboid = 2 (lb + bh + hl) = 2[(2x . x) + (x . x) + (x . 2x)]
= 2[(2 × 4 × 4) + (4 × 4) + (4 × 2 × 4)] cm2
= 2 [32 + 16 + 32] cm2 = 2[80] cm2 = 160 cm2.
Q.2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Sol. For cylindrical part:
Radius (r) = 7 cm
Height (h) = 6 cm
∴ Curved surface area
= 2πrh
For hemispherical part:
Radius (r) = 7 cm
∴ Surface area = 2πr2
∴ Total surface area
= (264 + 308) cm2 = 572 cm2.