Ajay is a Class X student. His class teacher Mrs Kiran arranged a historical trip to great Stupa of Sanchi. She explained that Stupa of Sanchi is great example of architecture in India. Its base part is cylindrical in shape. The dome of this stupa is hemispherical in shape, known as Anda. It also contains a cubical shape part called Hermika at the top. Path around Anda is known as Pradakshina Path.

Based on the above information, answer the following questions.
(i) Find the lateral surface area of the Hermika, if the side of cubical part is 8 m.

(ii) The diameter and height of the cylindrical base part are respectively 42 m and 12 m. If the volume of each brick used is 0.01 m³, then find the number of bricks used to make the cylindrical base.

(iii) If the diameter of the Anda is 42 m, then the volume of the Anda is

(iv) The radius of the Pradakshina path is 25 m. If Buddhist priest walks 14 rounds on this path, then find the distance covered by the priest.

(v) The curved surface area of the Anda is

One day Rinku was going home from school, saw a carpenter working on wood. He found that he is carving out a cone of same height and same diameter from a cylinder. The height of the cylinder is 24 ern and base radius is 7 cm. While watching this, some questions came into Rinkus mind. Help Rinku to find the answer of the following questions.

(i) After carving out cone from the cylinder,

(ii) Find the slant height of the conical cavity so formed.

(iii) The curved surface area of the conical cavity so formed is

(iv) External curved surface area of the cylinder is

(v) Volume of conical cavity is

To make the learning process more interesting, creative and innovative, Amayras class teacher brings clay in the classroom, to teach the topic - Surface Areas and Volumes. With clay, she forms a cylinder of radius 6 ern and height 8 cm. Then she moulds the cylinder into a sphere and asks some questions to students.

(i) The radius of the sphere so formed is 

(ii) The volume of the sphere so formed is

(iii) Find the ratio of the volume of sphere to the volume of cylinder.

(iv) Total surface area of the cylinder is 

(v) During the conversion of a solid from one shape to another the volume of new shape will 

A carpenter used to make and sell different kinds of wooden pen stands like rectangular, cuboidal, cylindrical, conical. Aarav went to his shop and asked him to make a pen stand as explained below. Pen stand must be of the cuboidal shape with three conical depressions, which can hold 3 pens. The dimensions of the cuboidal part must be 20 cm x 15 cm x 5 cm and the ffrlog radius and depth of each conical depression must be 0.6 cm and 2.1 cm respectively.

Based on the above information, answer the following questions.
(i) The volume of the cuboidal part is

(ii) Total volume of conical depressions is 

(iii) Volume of the wood used in the entire stand is

(iv) Total surface area of cone of radius r is given by

(v) If the cost of wood used is Rs 5 per cm³, then the total cost of making the pen stand is

Meera and Dhara have 12 and 8 coins respectively each of radius 3.5 cm and thickness 0.5 cm. They place their coins one above the other to form solid cylinders .

Based on the above information, answer the following questions.
(i) Curved surface area of the cylinder made by Meera is

(ii) The ratio of curved surface area of the cylinders made by Meera and Dhara is

(iii) The volume of the cylinder made by Dhara is

(iv) The ratio of the volume of the cylinders made by Meera and Dhara is

(v) When two coins are shifted from Meeras cylinder to Dhara's cylinder, then