A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm respectively. Find
(i) the volume of water which can completely fill the bucket;
(ii) the area of the metal sheet used to make the 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