Q. 3

# A metallic bucket

Given: Height of bucket = h = 24 cm

Radius of lower circular end = r = 7 cm

Radius of upper circular end = R = 14 cm

Total surface area of frustum = πr2 + πR2 + π(R + r)l cm2

Where l = slant height

l = 25 cm

(i) volume of water which will completely fill the bucket = volume of frustum

= 8 × 22 × 49

= 8722 cm3

volume of water which will completely fill the bucket = 8722 cm3

(ii) area of metal sheet used

Since the top is open we need to subtract the area of top/upper circle from total surface area of frustum because we don’t require a metal plate for top.

Radius of top/upper circle = R

Area of upper circle = πR2

area of metal sheet used = (total surface area of frustum)-πR2

Area of metal sheet used = πr2 + πR2 + π(R + r)l-πR2cm2

= πr2 + π(R + r)l cm2

= 22 × 82 cm2

= 1804 cm2

Area of metal sheet used to make bucket = 1804 cm2

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