Q. 3

(i) the volume of water which can completely fill the bucket;

(ii) the area of the metal sheet used to make the bucket.

Answer :

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 = πr^{2} + πR^{2} + π(R + r)l cm^{2}

Where l = slant height

∴ l = 25 cm

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

= 8 × 22 × 49

= 8722 cm^{3}

∴ volume of water which will completely fill the bucket = 8722 cm^{3}

(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 = πR^{2}

∴ area of metal sheet used = (total surface area of frustum)-πR^{2}

∴ Area of metal sheet used = πr^{2} + πR^{2} + π(R + r)l-πR^{2}cm^{2}

= πr^{2} + π(R + r)l cm^{2}

= 22 × 82 cm^{2}

= 1804 cm^{2}

∴ Area of metal sheet used to make bucket = 1804 cm^{2}

Rate this question :

How useful is this solution?

We strive to provide quality solutions. Please rate us to serve you better.

PREVIOUSThe radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm and its height is 8 cm. Find its total surface area. [Use π = 3.14.]NEXTA container, open the top, is in the form of a frustum of a cone of height 24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 24 per litre.

RELATED QUESTIONS :

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.

RS Aggarwal - MathematicsThe slant height of a bucket is 45 cm and the radii of its top and bottom are 28 cm and 7 cm respectively. The curved surface area of the bucket is

RS Aggarwal - MathematicsThe radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is

RS Aggarwal - MathematicsThe diameter of two circular ends of a bucket are 44 cm and 24 cm, and the height of the bucket is 35 cm. The capacity of the bucket is

RS Aggarwal - MathematicsA bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm^{3} of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket. (Use π = 3.14.)

A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left over is called

RS Aggarwal - Mathematics

The shape of a glass (tumbler) is usually in the form of

RS Aggarwal - Mathematics

Match the following columns: