Q30 of 47 Page 1

From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

Height of solid cylinder, h = 2.8 cm

Diameter of solid cylinder = 4.2 cm


So, radius of solid cylinder, r = 4.2/2 = 2.1 cm


We know that the relation between slant height, radius and height is


⇒ l =


⇒ l =


⇒ l = √12.25


∴ l = 3.5 cm


Here Total surface area of remaining solid = Curved surface area of cylinder + Area of base + Curved surface area of cone


We know that C.S.A of cylinder = 2πrh,


Area of base = πr2


And C.S.A of cone = πrl


⇒ T.S.A of remaining solid = 2πrh + πr2 + πrl


= πr (2h + r + l)


Substituting the values,


= π (2.1) (2(2.8) + 2.1 + 3.5)


= (22/7) (23.52)


∴ T.S.A. = 73.92 cm2


Ans. The total surface area of remaining solid is 73.92 cm2.


More from this chapter

All 47 →
28

Prove that a parallelogram circumscribing a circle is a rhombus.

 29

Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of the top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

 31

A peacock is sitting on the top of a pillar, which is 9 m high. From a point 27 m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught?

 10

The first and last terms of an AP are 7 and 49 respectively. If the sum of all its terms is 420, find its common difference.