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Question
A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm, and height 3 cm. Find the area of its whole surface and volume.
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Solution
The radii of the bottom and top circles are r1 = 10 cm and r2 = 6 cm respectively. The height of the frustum cone is h= 3 cm. Therefore, the volume of the bucket is
`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`
`=1/3pi(10^2+10xx6+6^2)xx3`
= 616 cm3
Hence Volume = 616 cm3
The slant height of the bucket is
`l=sqrt((r_1-r_2)+h^2)`
`=sqrt((10-6)^2+3^2)`
`=sqrt(25)`
= 5cm
The total surface area of the frustum cone is
`pi(r_1+r_2)xxl+pir_1_pir_2^2`
`=22/7xx(10+6)xx5+22/7xx10^2+22/7xx6^2`
`=4752/7`Square cm
= 678.85 Square cm
Hence Total surface area = 678.85
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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.
The ratio of total surface area of a solid hemisphere to the square of its radius is ______.
