A sandglass is a device used to measure time. It is also known as an hour glass, sand
timer or sand clock. Generally, It consists of two glass Bulbs Placed one above the
other which are connected by a narrow tube.
A special sand glass is shown in fig. In it, two Cones A and B are placed in a
cylindrical tube such that their vertex touch each other inside the tube. The height
of the cylinder is 21cm and the diameter is 6cm.Both cone are identical
(a) The Capacity of each Cone is
(a) 144 cm2 (b) 121 cm2 (c) 99 cm2 (d)88cm2
(b) The outer surface are of cylinder glass is
(a) 268.36 cm2 (b)396.85 cm2
(c)401.69 cm2 (d)452.57 cm2
(c) The volume of the remaining portion of the cylinder is
(a) 255 cm2 (b)369 cm2
(c)409 cm2 (d)460 cm2
(d) The sum of areas of bases of cones is
(a) 56.57 cm2 (b)78.34 cm2
(c)84 (d)68.5 cm2
(e) Curved surface area of the cylindrical glass
(a) 272 cm2 (b)396 cm2
(c) 420 cm2 (d) none of these
Answers
Given :- Two Cones A and B are placed in a cylindrical tube such that their vertex touch each other inside the tube. The height of the cylinder is 21cm and the diameter is 6cm. Both cone are identical .
solution :-
since both coins are identical and they have same radius . so, their height will be same .
so,
→ Height of both cube = Height of cylinder /2 = 21/2 = 10.5 cm
then,
→ Capacity of each cone = (1/3)πr²h = (1/3) * (22/7) * (3)² * 10.5 = 22 * 3 * 1.5 = 99 cm³ .
now,
→ Curved surface area of cylinder = 2πrh = 2 * (22/7) * 3 * 21 = 396 cm² .
and,
→ Volume of remaining portion of the cylinder = Volume of cylinder - 2 * volume of cone = πr²h - 2 * 99 = (22/7) * 9 * 21 - 198 = 396 cm³ .
also,
→ Sum of areas of bases of cone = 2 * πr² = 2 * 3.14 * 9 = 56.52 cm² .
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