Arun a 10^th standard student makes a project on corona virus in science for an exhibition in his school. In this project, he picks a sphere which has volume 38808 cm³ and 11 cylindrical shapes, each of volume 1540 cm³ with length 10 cm.

Based on the above information, answer the following questions.
(i) Diameter of the base of the cylinder is

(ii) Diameter of the sphere is

(iii) Total volume of the shape formed is

(iv) Curved surface area of the one cylindrical shape is

(v) Total area covered by cylindrical shapes on the surface of sphere is

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

Ankit wants a beautiful ceramic cuboidal flower vase for the decoration of his room. So, he visit to ceramicists and explained him about, what kind of flower vase he wants. According to his requirement, the ceramicists carved out a sphere of maximum size from a cuboidal ceramic block of dimensions 24 cm by 24 cm by 27 cm.

Based on the above information, answer the following questions.
(i) What is the maximum radius of the sphere that can be carved out from the block of ceramic?

(ii) What is the volume of the complete block of ceramic?

(iii) What is the volume of the ceramic carved out?

(iv) What is the volume of the cuboidal vase thus formed?

(v) What is the surface area of the sphere carved out?

Pankaj's father has to purchase a new water tank to store water for irrigation of their fields. For this purpose, they visit to a shop. The shopkeeper has three types of water tanks as shown below.

Based on the above information, answer the following questions.
(i) If the radius of type- I tank is 1.5 m and its height is 3.5 m, then find the capacity of tank type- I. (Take \(\pi\): = 3.14)

(ii) Find the capacity of type- II tank having dimensions 5 m x 4 m x 3.5 m

(iii) How much more water type- III tank contains than tank of type- I, if its base radius is 2.5 m and total height is 5.5 m? [Take \(\pi\) = 3.14]

(iv) If Pankaj's father bought type- II tank and wants to cover it with a cloth costs Rs 45 per m², then find the total cost of cloth used (if cloth is covered on all its faces).

(v) Find the ratio of the total surface area of type- I and type-Il tanks.

Emily purchased a spinner from a shop, which is of the shape as shown in the figure, in which right circular cone and hemisphere lie on opposite sides of a common base of length 3.5 m. Cylindrical box circumscribing them in this position. Now, answer the following questions.

(i) What will be the volume of the cone?

(ii) Volume of hemispherical part is

(iii) Volume of cyiinder that circumscribe the cone and hemisphere, is

(iv) Find the additional space enclosed by the cylinder.

(v) Find the ratio of the curved surface areas of cone and hemisphere.

Pinki's class teacher explained the students about the benefits of drinking fruit juice in the morning. So, Pinki went to a juice stall with her friend Bipin. On the stall, they observed that shopkeeper has three types of glasses of inner diameter 4.6 cm to serve customers. The height of each glass is 11 cm. Seeing this, certain questions came into their mind. Help Pinki and Bipin to solve these questions.

(i) Volume of the type (A) glass is

(ii) Volume of type (B) glass is 

(iii) How much more juice can be filled in type (A) glass than glass of type (C)?

(iv) Which glass has minimum capacity?

(v) Which mathematical concept has been used in above problem?

Anjali join four cubical open boxes of edge 20 cm each to make a pot for planting saplings of pudina in her kitchen garden, The saplings are cylindrical in shape with diameter 14.2 cm and height 11 cm.

On the basis of above information, answer the following questions.
(i) If Anjali wants to paint the outer surface of the pot, then how much area she needs to paint?

(ii) What is the volume of the pot formed?

(iii) If Anjali decorates the four walls of the pot with coloured square paper of side 10 cm each, then how many pieces of papers would be required?

(iv) Find the volume of 1 sapling.

(v) If Anjali planted 4 saplings in the pot with some soil and compost up to the brim of the pot, then how much soil and compost are there in the pot?

Ritu packed a football as a gift for her brother's birthday in a cuboidal box whose diameter is same as that of length of base of the box having length, breadth and height respectively 23 cm, 23 cm and 28 cm.

(i) The volume of the football is

(ii) Ritu covers the box with a wrapping sheet. The area of the wrapping sheet that covers the box exactly is

(iii) The volume of the box is

(iv) Half of the remaining volume of the box is filled with thermocol balls. Find the volume of thermocol balls used.

(v) The surface area of the football is

Alok and his family went for a vacation to Iaipur, There they had a stay in tent for a night. Alok found that the tent in which they stayed is in the form of a cone surmounted on a cylinder. The total height of the tent is 42 m, diameter of the base is 42 m and height of the cylinder is 22 m.

Based on the above information, answer the following questions.
(i) How much canvas is needed to make the tent?

(ii) If each person needs 126 m² of floor, then how many persons can be accommodated in the tent?

(iii) Find the cost of the canvas used to make the tent, if the cost of 100 m² of canvas is Rs 425.

(iv) Find the volume of the tent.

(v) Find the number of persons that can be accommodated in tent, if each person needs 1892 m³ of space.

Isha's father brought an ice-cream brick, empty cones and scoop to pour the ice-cream into cones for all the family members. Dimensions of the ice-cream brick are (30 x 25 x 10) cm³ and radius of hem i-spherical scoop is 3.5 cm. Also, the radius and height of cone are 3.5 cm and 15 cm respectively.

Based on the above information, answer the following questions.
(i) The quantity of ice-cream in the brick (in litres) is

(ii) Volume of hemispherical scoop is

(iii) Volume of a cone is

(iv) The minimum number of scoops required to fill one cone upto brim is

(v) The number of cones that can be filled upto brim using the whole brick is

Arpana is studying in X standard. While helping her mother in kitchen, she saw rolling pin made of steel and empty from inner side, with two small hemispherical ends as shown in the figure.

(i) Find the curved surface area of two identical cylindrical parts, if the diameter is 2.5 cm and length of each part is 5 cm.

(ii) Find the volume of big cylindrical part.

(iii) Volume of two hemispherical ends having diameter 2.5 cm, is

(iv) Curved surface area of two hemispherical ends, is

(v) Find the difference of volumes of bigger cylindrical part and total volume of the two small hemispherical ends.