Answer :

Explanation: Here the bucket is in the shape of a frustum. So capacity of bucket will be equal to the volume of the frustum and in order to calculate the total surface area of the bucket we will subtract the top end circular area from the total surface area of the frustum as the bucket is open on top.


Upper end radius of frustum/bucket = R = 28 cm


Lower end radius of frustum/bucket =r = 7 cm


Height of the frustum/bucket = 28 cm


And we know,


The capacity of bucket = Volume of the bucket


And, Volume of bucket = Volume of Frustum


Capacity of bucket = Volume of frustum


Volume of frustum


Where R = Radius of larger or upper end and r = Radius of smaller or lower end and h = height of frustum π = 22/7


Volume of frustum




= 22 × 4 × 343


Volume of frustum = 30184 cm3


Capacity of bucket = 30184 cm3


T.S.A of bucket = T.S.A of frustum – Area of upper circle eqn1


Let the slant height of the frustum be ‘ℓ’ cm


So, ℓ2 = h2 + (R – r)2


2 = 282 + (28 – 7)2


2 = 784 + (21)2


2 = 784 + 441


2 = 1225


ℓ = √(1225)


ℓ = 35 cm


T.S.A of frustum = π(R + r)ℓ + πR2 + πr2


= π(28 + 7) × 35 + π(28)2 + π(7)2


= 35 × 35π + 784π + 49π


= 1225π + 784π + 49π eqn2


Area of upper circle = πR2


= π(28)2


= 784π eqn3


T.S.A of bucket = 1225π + 784π + 49π – 784π (from eqn2 and 3)


T.S.A of bucket = 1274π


T.S.A of bucket=


T.S.A of bucket = 182 × 22


T.S.A of bucket = 4004 cm2


The capacity and total surface area of the bucket is 30184 cm3 and 4004 cm2.


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