The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm respectively. Find the curved surface area of the bucket.
Given: slant height of bucket = l = 45 cm
Radius of bottom circle = r = 7 cm
Radius of top circle = R = 28 cm
As the bucket is in the form of frustum
Formula: Total surface area of frustum = πr2 + πR2 + π(R + r)l cm2
Now we have asked curved surface area, so we should subtract the top and bottom surface
areas which are flat circles.
Surface area of top = πr2
Surface area of bottom = πR2
∴ Curved surface area = total surface area – πr2 - πR2 cm2
= πr2 + πR2 + π(R + r)l – πr2 - πR2 cm2
= π(R + r)l cm2
= 3.14 × (28 + 7) × 45 cm2
= 3.14 × 35 × 45 cm2
= 4945.5 cm2
Therefore, curved surface area of bucket = 4945.5 cm2