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Question
The radii of the circular bases of a frustum of a right circular cone are 12 cm and 3 cm and the height is 12 cm. Find the total surface area and the volume of the frustum.
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Solution
The height of the frustum cone is h= 12 cm. The radii of the bottom and top circles are r1 = 12cm and r2 = 3cm respectively.
The slant height of the frustum cone is
`l=sqrt((r_1-r_2)^2+h^2`
`=sqrt((12-3)^2+12^2`
`=sqrt(225)`
= 15 cm
The total surface area of the frustum cone is
`=pi(r_1+r_2)xxl+pir_2^2+pir_2^2`
`=pixx(12+3)xx15+pixx12^2+pixx3^2`
= π x 225 x 26 + 144π + 9π
= 378π cm2
Hence Total surface area = 378π cm2
The volume of the frustum cone is
`V=1/3pi(r_1^2+r_1r_2+r_2^2)xxh`
`=1/3pi(12^2+12xx3+3^2)xx12`
`=1/3xxpixx189xx12`
= 756π cm3
Hence Volume of frustum = 756π cm3
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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?
