Question

if the radii of the circular ends of a conical bucket which is 32cm high are 40cm and 16cm,find the capacity and total surface area of the bucket

Answer 1

Answer:

Volume = Capacity = = 83675.42 cubic cm.

Total Surface area = 7844.57 Square cm.

Step-by-step explanation:

Volume of bucket = Volume of the frustum = πh(R^2+Rr+r^2 )/3

Here R = 40 cm

r = 16 cm

h = 32 cm.

Volume of bucket = 22*32*(40*40 + 40*16 + 16*16)/(3*7) = 22 * 32 * 2496/(3*7)

= 83675.42 cubic cm.

The bucket is normally open from the top and closed from bottom. (Add area of bottom circle to lateral surface area)

Hence total surface area = π(R+r)*s+ πr^2

s = Slant height. = √((h^2+(R-r)^2) = √(32^2+(40-16)^2  = 40cm.

Hence Total surface area of the bucket = π(40+16)*40+ π16^2 = 7844.57 Square cm.

Answer 2

Answer:

Volume of Frustum of cone = 1/3 ×π×r*2 × h

TSA of Frustum of cone = π(R +r ) l + π ( R*2 + r*2 )