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Question
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?
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Solution
Given height of cone (h) = 4cm
Diameter of cone (d) = 6cm
∴Radius (r) =`6/2 =3 cm`
Let ‘l’ be slant height of cone
`l=sqrt(r^2+h^2)`
`=sqrt(3^2+4^2) =5cm`
l = 5cm
∴ Slant height of cone (l) = 5cm.
Curved surface area of cone (S1) = πrl
S1 = π(3)(5) = 47.1cm2
Curved surface area of hemisphere (S2) = 2πr2
`S_2=2pi(3)^2=56.52cm^2`
∴Total surface area(S) = S1 + S2
= 47.1 + 56.52
= 103.62cm2
∴ Curved surface area of toy = 103.62cm2
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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?
A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m2 of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m2.
