assume that
a minar rate is in the shape of a cylinder surmounted by a hemisphere are made using marble stone there are 4 min rate of uniform size and shape on the four corners and larger unit at the centre.
Minaret
radius at corners : 0.7m
radius at centre: 3.5m
full height (cy+hs)
at corners: 15.7m
at centre: 13.5m
1) destribe the monument with the given hint along with your collected idea and pictures. ?
2) taking idea of surface area and volume find out the volume of air in the 4 corner minarets.?
3) taking the idea of surface area and volume find out the cost of polishing the centre minaret at rate Rs.1000 per square metre.?
Answers
Given : A minaret is in the shape of a cylinder surmounted by a hemisphere made using marble stone.
Minaret radius Full height (cy+hs)
At corners 0.7 m 15.7 m
At centre 3.5 m 13.5m
4 minarets of uniform size and shape on the 4 corners and larger minaret at the centre.
To find : the volume of air in the 4 corner minarets
cost of polishing the centre minaret at rate Rs.1000 per square metre.?
Solution:
cy = cylinder
hs = hemisphere
Minaret at corner
radius = 0.7 m
Full height (cy+hs) = 15.7 m
cy height = 15.7 - 0.7 = 15 m
Outer surface area = 2πrh + 2πr²
= 2πr(h + r)
= 2(22/7)(0.7)(15.7)
= 69.08 m²
Area of 4 minarets = 4 x 69.08 = 276.32 m²
Volume = πr²h + (2/3)πr³
= πr²(h + 2r/3)
= (22/7)(0.7)²(15 + 2*0.7/3)
= 23.82 m³
volume of air in the 4 corner minarets. = 4 x 23.82 = 95.28 m³
Minaret at center
radius = 3.5 m
Full height (cy+hs) = 13.5 m
cy height = 13.5 - 3.5 = 10 m
Outer surface area = 2πrh + 2πr²
= 2πr(h + r)
= 2(22/7)(3.5)(13.5)
= 297 m²
cost of polishing the centre minaret at rate Rs.1000 per square metre
= 297 x1000 = 297000 Rs ( from out side only )
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