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Test: Surface Area & Volumes- Case Based Type Questions - EmSAT Achieve MCQ


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10 Questions MCQ Test Mathematics for EmSAT Achieve - Test: Surface Area & Volumes- Case Based Type Questions

Test: Surface Area & Volumes- Case Based Type Questions for EmSAT Achieve 2024 is part of Mathematics for EmSAT Achieve preparation. The Test: Surface Area & Volumes- Case Based Type Questions questions and answers have been prepared according to the EmSAT Achieve exam syllabus.The Test: Surface Area & Volumes- Case Based Type Questions MCQs are made for EmSAT Achieve 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Surface Area & Volumes- Case Based Type Questions below.
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Test: Surface Area & Volumes- Case Based Type Questions - Question 1

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?

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 1
Volume of the hemisphere

Test: Surface Area & Volumes- Case Based Type Questions - Question 2

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.

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 2
The formula for the volume of a cylinder is V = Bh or V = πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V = πr2h.
Test: Surface Area & Volumes- Case Based Type Questions - Question 3

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?

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 3
Required cloth material = 4 × Curved surface area of hemispherical domes

Test: Surface Area & Volumes- Case Based Type Questions - Question 4

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.

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 4
Curved surface area of the pillar = 2πrh

Test: Surface Area & Volumes- Case Based Type Questions - Question 5

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?

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 5

Test: Surface Area & Volumes- Case Based Type Questions - Question 6

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?

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 6
Circumference of the base of the dome

= 2πr

= 2π(22)

= 44π

Test: Surface Area & Volumes- Case Based Type Questions - Question 7

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?

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 7
Diameter = 44 m

Radius = 22 m

Curved surface area of hemispherical dome

= 2πr2

= 2π(22)2

= 968π m2

Test: Surface Area & Volumes- Case Based Type Questions - Question 8

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?

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 8
Total height of monument = 51 m

Radius of hemispherical dome part = height of hemispherical dome = 22 m

Height of the cuboidal part = 51 m – 22m

= 29 m

Test: Surface Area & Volumes- Case Based Type Questions - Question 9

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.

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 9
Curved surface area of hemispherical dome

= 968p m2

Cost of painting 100 cm2 = ₹ 10

Cost of painting 1 m2 = ₹ 1000

Thus, cost of painting the dome

= ₹ 1000 × 968π cm2

= ₹ 968000π

Test: Surface Area & Volumes- Case Based Type Questions - Question 10

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?

Detailed Solution for Test: Surface Area & Volumes- Case Based Type Questions - Question 10
Area of a cube = 2(lb + bh + hl).
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