Mathematics teacher of a school took her 9th standard students to show Gol Gumbaz. It was a part of their Educational trip. The teacher had interest in history as well. She narrated the facts of Gol Gumbaz to students. Gol Gumbaz is the tomb of king Muhammad Adil Shah, Adil Shah Dynasty. Construction of the tomb, located in Vijayapura , Karnataka, India, was started in 1626 and completed in 1656. It reaches up to 51 meters in height while the giant dome has an external diameter of 44 meters, making it one of the largest domes ever built. At each of the four corners of the cube is a dome shaped octagonal tower seven stories high with a staircase inside.

(a) What is the total surface area of a cuboid?

(b) What is the curved surface area of hemispherical dome ?

(c) What is the height of the cubodial part ?

d) What is the circumference of the base of the dome ?

(v) The total surface area of a hemispherical dome having radius 7 cm is:

Mathematics teacher of a school took his 10th standard students to show Taj Mahal. It was a part of their Educational trip. The teacher had interest in history as well. He narrated the facts of Taj Mahal to the students. Then the teacher said in this monument one can find combination of solid figures. There are 4 pillars which are cylindrical in shape. Also, 2 domes at the back side which are hemispherical. 1 big domes at the centre. It is the finest example of the symmetry. (Use π = 22/7)
(i)How much cloth material will be required to cover 2 small domes each of radius 4.2 metres?

(ii) Write the formula to find the volume of one pillar (including hemispherical dome) :

(iii) The volume of the hemispherical dome at the centre if base radius is 7 m is :

(iv) What is the lateral surface area of all 4 pillars if height of the each pillar is 14 m and base radius is 1.4 m (without dome)?

(v) The cost of polishing all the four pillars if the cost of 1 m² is Rs. 270, will be :

Mathematics teacher of a school took his 10th standard students to show Taj Mahal. It was a part of their Educational trip. The teacher had interest in history as well. He narrated the facts of Taj Mahal to the students. Then the teacher said in this monument one can find combination of solid figures. There are 4 pillars which are cylindrical in shape. Also, 2 domes at the back side which are hemispherical. 1 big domes at the centre. It is the finest example of the symmetry. (Use π = 22/7)
(i)How much cloth material will be required to cover 2 small domes each of radius 4.2 metres?

(ii) Write the formula to find the volume of one pillar (including hemispherical dome) :

(iii) The volume of the hemispherical dome at the centre if base radius is 7 m is :

(iv) What is the lateral surface area of all 4 pillars if height of the each pillar is 14 m and base radius is 1.4 m (without dome)?

(v) The cost of polishing all the four pillars if the cost of 1 m² is Rs. 270, will be :

Mathematics teacher of a school took her 9th standard students to show Red fort. It was a part of their Educational trip. The teacher had interest in history as well. She narrated the facts of Red fort to students. Then the teacher said in this monument one can find combination of solid figures. There are 2 pillars which are cylindrical in shape. Also 2 domes at the corners which are hemispherical.7 smaller domes at the centre. Flag hoisting ceremony on Independence Day takes place near these domes.

(i) How much cloth material will be required to cover 2 big domes each of radius 2.5 metres?

(ii) Write the formula to find the volume of a cylindrical pillar:

(iii) Find the lateral surface area of two pillars if height of the pillar is 7 m and radius of the base is 1.4 m.

(iv) How much is the volume of a hemisphere if the radius of the base is 3.5 m?

(v) What is the ratio of sum of volumes of two hemispheres of radius 1 cm each to the volume of a sphere of radius 2 cm?

An architect's planned design for a room with dimensions of 8.6 m, 5.4 m and 4 m respectively. He also planned to make 4 windows with blue colour and 2 doors with brown wood colour. The room needs to be painted with Asian paint of Green colour except for the floor and square tiles were used for flooring as shown in the below figure:

(i) The total area of the four walls is :

(ii) If the area of windows and doors is 22 sq m.  The area of the walls to be painted

(iii) What is the area of the tiles to be used for flooring?

(iv) The total area of the room is (including windows and doors):

(v) What is the volume of the air in the room?

Mohan lives in Hyderabad in Telangana. Those were very hot days of May. He thought that if we human beings need so much of water to drink, won’t the birds also be thirsty. He decided to prepare a vessel to provide water for birds. He found a flexible blue coloured plastic rectangular sheet 44 cm × 15 cm. He rolled it along its length and joined the two opposite ends using a tape. He wanted to have a circular base for this cylinder and searched for another sheet. He found a square sheet 15 cm × 15 cm. He got a circular sheet just equal to the base of the cylinder cut from it. 15 cm 44 cm 15 cm 15 cm

(a) The curved surface area of the cylinder formed is

(b) The radius of the base of the cylinder is

(c) The area of the circular base required for the cylinder is

(d) How much will be the area of square sheet left unused after removing the circular base of the cylinder from it?

(e) Find the volume of water that can be filled in the cylinder.

Mr. Kumar, a Mathematics teacher brings some green coloured clay in the classroom to teach the topic 'mensuration'. First, he forms a cylinder of radius 6 cm and height 8 cm with the clay. Then, he moulds that cylinder into a sphere similarly, he moulds the sphere in other different shapes. Answer the following questions:
(i) Which of the following is not a 3D shape?

(ii) What is the volume of cylindrical shape?

(iii) What is the formula of volume of sphere?

(iv) When clay changes into on shape to other which of the following remains same. 

(v) The radius of the sphere formed is :

In a newly constructed park which is situated in the heart of a city Hyderbad, an architect has form a structure in the given shape. The shape has a cuboid, which is standing on the two cylindrical beams. The dimensions of the cuboid are 1.5 m, 3 m and 0.5 m. The dimensions of the cylinders are of height 2 m and diameter 0.6 m.

(i) As the structure is made from the concrete, how much volume of concrete is reqired to make the cuboidal shape?

(ii) What is formula for calculating the lateral surface area of the cylinder?

(iii) What is the volume of two cylinders?

(iv) If the cuboid needs to be painted red, how much area need to be painted?

(v)  If a cloth is needed to cover the cylindrical part, how much cloth is needed?

One day teacaher planned to take all the Class X students to the milk factory (Chilling plant) and asked the students to observe it carefully. Refer to this plant, its machinery is shown below. It is related to some solid shapes, which we study in our curriculum.

(i) Refer to cylindrical container, calculate the quantity of milk it can store.

(ii) What is the formula for calculating the total surface area of the cylindrical container i.e., milk container?

(iii) If the cube shown in the picture is of dimension 6 cm each. Find the capacity of this cubic container.

(iv) Find the ratio between the volume and C.S.A. of the cylindrical container.

(v)  What is the formula for calculating the total surface area of the hemisphere?