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Question
If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is ______.
Options
xyz
2xyz
`sqrt("xyz")`
`root(3)("xyz")`
Solution
If the areas of three adjacent faces of a cuboid are x, y and z, respectively, the volume of the cuboid is `underline(sqrt("xyz"))`.
Explanation:
Let the length of the cuboid = l
breadth of the cuboid = b
and height of the cuboid = h
Since, the areas of the three adjacent faces are x,
and z, we have:
lb = x
bh = y
lh = z
Therefore,
lb × bh × lh = xyz
⇒ l2 b2 h2 = xyz
⇒ lbh = `sqrt(xyx)`
Hence, the volume of the cuboid = lbh = `sqrt(xyz)`
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Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work which has attracted Indians as well as foreigners with a variety of tea sets, crockery and ceramic tile works. A huge portion of the ceramics used in the country is supplied by Khurja and is also referred as "The Ceramic Town". One of the private schools of Bulandshahr organised an Educational Tour for class 10 students to Khurja. Students were very excited about the trip. Following are the few pottery objects of Khurja.
Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. |
Maths teacher who was accompanying the students asked the following questions:
- The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and the radius and height of the cylindrical jar in II are 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required?
- If in the cylindrical jar full of water, a conical funnel of the same height and same diameter is immersed, then how much water will flow out of the jar?
Statement A (Assertion): Total Surface area of the top is the sum of the curved surface area of the hemisphere and the curved surface area of the cone.
Statement R( Reason): Top is obtained by joining the plane surfaces of the hemisphere and cone together.
