A tree trunk I metres long, is in the shape of a frustum of a cone, the radii of its ends being a and meters `(a > b).` It is required to cut from it a beam of uniforms quare section. Prove that the beam of the greatest volume that can be cut is `1/3 (al)/(a-b)` metres long.

A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 9 cm respectively. (i) Calculate the height of the cone of which the bucket is a part. (ii) The volume of water which can be filled in the bucket. (iii) The area of copper sheet required to make the bucket.

A bucket of height 8 cm and made up of copper sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 9 cm respectively. Calculate the height of the cone of which the bucket is a part. the volume of water which can be filled in the bucket. (iii) the area of copper sheet required to make the bucket.

A container opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper end as 8 cm and 20 cm, respectively. Find the cost of made which can completely fill the container, at the rate of Rs 20 per litre. Also find the cost of metal shape used to make the container, if it costs Rs 8 per 16cm^(2) . (Take pi=3.14 )

How many pieces each 5""1/6 metres long can be cut from a cloth 77""1/2 metres long?

A bucket of height 8 cm and made up of a copper sheet is in the form of frustum of a right circular cone with radii of its upper and lower ends being 3 cm and 9 cm respectively. Calculate. A] The height of the cone of which the bucket is a part. B] Volume of water which can be filled in the bucket C] The area of copper sheet required to make the bucket.

A ribbon is 42 metres long. How many pieces each of length 1""3/4 metres can be cut from it ?

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459 3/7 cm^2 . The radii of its lower and upper circular ends are 8 cm and 20 cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs. 1.40 per square centimeter.

A milk container is made of metal sheet in the shape of frustum of a cone whose volume is 10459(3)/(7)cm^(2). The radii of its lower and upper circular ends are 8cm and 20cm respectively. Find the cost of metal sheet used in making the container at the rate of Rs.1.40per square centimeter.

How many pieces of equal size can be cut from a rope of 30 metres long,each measuring 3(3)/(4) metres?

The vertical section of a road over a canal bridge in the direction of its length is in the form of circle of radius 8.9 metre. Then the greatest spped at which the car can cross this bridge wihout losing contact with the road at its hgihest point, the centre of gravity of the car being at a height h = 1.1 metre from the ground. Take g = 10 m/sec2-