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प्रश्न
A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π =`22/7`)
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उत्तर
Given,
Radius of the common base(r) = 3.5 cm
Height of the cylindrical part (h) = 10 cm
Height of the conical part (H) = 6 cm
Let 'l' be the slant height of the cone
Then, we know that,
I2 = r2 + H2
I2 = 3.52 + 62
= 12.25 + 36
= 48.25
l = 6.95 cm
So, the curved surface area of the cone (S1) = πrl
S1 = π(3.5)(6.95)
S1 = `22/7 xx 3.5 xx 6.95`
S1 = 76.45 cm2
Curved surface area of cylinder (S2) = 2πrh
S2 = 2π(3.5)(10)
S2 = `2 xx 22/7 xx 3.5 xx 10`
S2 = 220 cm2
Curved surface area of hemisphere(S3) = 2πr2
S3 = `2 xx 22/7 xx 3.5^2`
S3 = 77 cm2
Total surface area of the solid is given by
S = S1 + S2 +S3
= 76.45 + 220 + 77
= 373.45 cm2
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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?
