Surface Area & Volumes- Case Based Type Questions - Free with solutions

A school organised an educational trip to Taj Mahal. Mathematics teacher of the school took her 9th standard students to it. The teacher had interest in history as well. She narrated the facts to Taj Mahal to students. Then the teacher said in this monument one can find combination of solid figures. There are 4 pillars which are cylindrical in shape. The Taj Mahal has a larger white dome surrounded by four smaller domes.

Q. How much is the volume of a hemisphere if the radius of the base is 3.5 m?

A school organised an educational trip to Taj Mahal. Mathematics teacher of the school took her 9th standard students to it. The teacher had interest in history as well. She narrated the facts to Taj Mahal to students. Then the teacher said in this monument one can find combination of solid figures. There are 4 pillars which are cylindrical in shape. The Taj Mahal has a larger white dome surrounded by four smaller domes.

Q. Write the formula to find the volume of a cylindrical pillar.

A school organised an educational trip to Taj Mahal. Mathematics teacher of the school took her 9th standard students to it. The teacher had interest in history as well. She narrated the facts to Taj Mahal to students. Then the teacher said in this monument one can find combination of solid figures. There are 4 pillars which are cylindrical in shape. The Taj Mahal has a larger white dome surrounded by four smaller domes.

Q. How much cloth material will be required to cover 4 small domes each of radius 2 m?

A school organised an educational trip to Taj Mahal. Mathematics teacher of the school took her 9th standard students to it. The teacher had interest in history as well. She narrated the facts to Taj Mahal to students. Then the teacher said in this monument one can find combination of solid figures. There are 4 pillars which are cylindrical in shape. The Taj Mahal has a larger white dome surrounded by four smaller domes.

Q. Find the curved surface area of the pillar its height is 7 m and radius of its base is 1.4 m.

A school organised an educational trip to Taj Mahal. Mathematics teacher of the school took her 9th standard students to it. The teacher had interest in history as well. She narrated the facts to Taj Mahal to students. Then the teacher said in this monument one can find combination of solid figures. There are 4 pillars which are cylindrical in shape. The Taj Mahal has a larger white dome surrounded by four smaller domes.

Q. What is the ratio of volume of hemisphere of radius 1 cm to the volume of a cylinder with radius 2 cm and height 1 cm?

Nikita has to make her project on 'Monument in India'. She decided to make her project on Gol Gumbaz monument. She already knows following things about it :

• It is located in a small town in Northern Karnataka.
• 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.

Help her in making project by answering the following questions :

Q. What is the circumference of the base of the dome?

Nikita has to make her project on 'Monument in India'. She decided to make her project on Gol Gumbaz monument. She already knows following things about it :

• It is located in a small town in Northern Karnataka.
• 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.

Help her in making project by answering the following questions :

Q. What is the curved surface area of hemispherical dome?

Nikita has to make her project on 'Monument in India'. She decided to make her project on Gol Gumbaz monument. She already knows following things about it :

• It is located in a small town in Northern Karnataka.
• 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.

Help her in making project by answering the following questions :

Q. What is the height of the cuboidal part?

Nikita has to make her project on 'Monument in India'. She decided to make her project on Gol Gumbaz monument. She already knows following things about it :

• It is located in a small town in Northern Karnataka.
• 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.

Help her in making project by answering the following questions :

Q. Find the cost of painting the dome, given the cost of painting is ₹ 100 per cm².

Nikita has to make her project on 'Monument in India'. She decided to make her project on Gol Gumbaz monument. She already knows following things about it :

• It is located in a small town in Northern Karnataka.
• 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.

Help her in making project by answering the following questions :

Q. What is the area of a cube?