Question

17) Case study -1:
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 figure
In it two cones A and B are placed in a cylindrical tube such that their vertex touches
each other inside the tube.
GA
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Answer 1

Answer:

Sum of areas of bases of cone = 2 * πr² = 2 * 3.14 * 9 = 56.52 cm² .

Step-by-step explanation:

Step 1: 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 .

Since both coins are identical and they have same radius . so, their height will be same .

so,

Step 2: 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,

Step 3: 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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