A bucket is in the form of a frustum of a cone whose radii of bottom and top are 7 cm and 28cm repectively. of the capacity of bucket is 21560cmcube ,find the total surface area of bucket
Answers
Answer:
Total Surface Area = 3190cm^2
Step-by-step explanation:
Top radius of frustum (R) = 28cm
Bottom radius of frustum (r) = 7cm
Volume of frustum = 21560cm^3
Therefore,
Vol. of frustum = πh/3 { R^2 + r^2 +Rr}
=> 21560 = πh/3 {(28)^2 + (7)^2 + (28)(7)}
=> 64680 = h { 784 + 49 + 196}
=> (64680×7)/22 = 1029h
=> 2940 × 7 = 1029h
=> h = 20580 ÷ 1029
=> h = 20cm
Now, slant height(l)
(l)^2 = h^2 + (R - r) ^2
= 20^2 + (28 - 7)^2
= 400 + 21^2
= 400 + 441
= 841
=> l = √841
= 29cm
=> TSA of bucket = ( lateral surface area ) + ( area of the bottom )
= πl (R + r) + πr^2
= π { l ( R+r ) + r^2 }
= π { 29(28+7) + 7^2 }
= π ( 29×35 + 49 )
= π ( 1015 )
= 22/7 × 1015
=22 × 145
=3190cm^2
Hence, the total surface area of the bucket is 3190cm^2. ---> ANS
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