ANNUAL EXAM PYQS · CHAPTER 11

Surface Areas and Volumes
CBSE Most Repeated PYQs

Solve official Class 9 Annual Examination Questions for Surface Areas and Volumes. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1Annual Exam 2024MCQ

1 Mark

Curved surface area of a right circular cone of radius r and slant height l is:

Q2Annual Exam 2023MCQ

1 Mark

Surface area of a sphere of radius r is:

Q3CBSE Pattern PYQMCQ

1 Mark

Volume of a sphere of radius r is:

Q4Annual Exam 2022MCQ

1 Mark

Slant height l of a cone with radius r and height h is:

Q5CBSE Model PYQAssertion-Reason

1 Mark

Assertion (A): Total surface area of a cone of radius r and slant height l is πr(l + r). Reason (R): Total surface area includes curved surface area πrl and base area πr².

Q6Annual Exam 2021Assertion-Reason

1 Mark

Assertion (A): Volume of a hemisphere of radius r is (2/3)πr³. Reason (R): A hemisphere is exactly half of a solid sphere.

Q7Annual Exam 2024Short Answer

2 Marks

Find diameter of base of cone if its slant height is 14 cm and CSA is 308 cm².

Q8Annual Exam 2023Short Answer

2 Marks

Find surface area of a sphere of radius 7 cm.

Q9CBSE Pattern PYQShort Answer

2 Marks

Find volume of a sphere whose radius is 3.5 cm.

Q10Annual Exam 2022Short Answer

2 Marks

Find total surface area of a hemisphere of radius 10 cm (use π = 3.14).

Q11CBSE Model PYQShort Answer

2 Marks

A conical tent is 10 m high and radius of base is 24 m. Find its slant height.

Q12Annual Exam 2021Long Answer

3 Marks

A bus stop is barricaded from remaining road by 50 hollow cones made of recycled cardboard. Base diameter is 40 cm and height is 1 m. Find cost of painting at ₹12/m² (π=3.14, √1.04=1.02).

Q13Annual Exam 2024Long Answer

3 Marks

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find cost of tin-plating on inside at ₹16 per 100 cm².

Q14Annual Exam 2023Long Answer

3 Marks

A dome of a building is in form of hemisphere. From inside, it was white-washed at cost of ₹498.96. If rate is ₹2/m², find (i) inside surface area (ii) volume of air inside.

Q15CBSE Pattern PYQLong Answer

3 Marks

Twenty seven solid iron spheres of radius r and surface area S are melted to form a sphere with surface area S'. Find (i) radius r' of new sphere (ii) ratio of S and S'.

Q16Annual Exam 2022Case Study

4 Marks

Case Study Scenario: A conical heap of wheat has diameter 10.5 m and height 3 m. Question: Find its volume and canvas area needed to cover it.

Q17CBSE Model PYQCase Study

4 Marks

Case Study Scenario: The moon's diameter is approximately one-fourth of diameter of earth. Question: Find ratio of their surface areas and volumes.

Q18Annual Exam PYQPYQ

5 Marks

A hemispherical tank is full of water. It is emptied by a pipe at rate of 3 4/7 litres per second. How much time will it take to empty half tank if diameter is 3 m?

Q19Annual Exam PYQPYQ

5 Marks

A capsule of medicine is in shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?

Q20Annual Exam PYQPYQ

5 Marks

Surface Areas and Volumes CBSE Most Repeated PYQs

Curved surface area of a right circular cone of radius r and slant height l is:

Surface area of a sphere of radius r is:

Volume of a sphere of radius r is:

Slant height l of a cone with radius r and height h is:

Assertion (A): Total surface area of a cone of radius r and slant height l is πr(l + r). Reason (R): Total surface area includes curved surface area πrl and base area πr².

Assertion (A): Volume of a hemisphere of radius r is (2/3)πr³. Reason (R): A hemisphere is exactly half of a solid sphere.

Find diameter of base of cone if its slant height is 14 cm and CSA is 308 cm².

Find surface area of a sphere of radius 7 cm.

Find volume of a sphere whose radius is 3.5 cm.

Find total surface area of a hemisphere of radius 10 cm (use π = 3.14).

A conical tent is 10 m high and radius of base is 24 m. Find its slant height.

A bus stop is barricaded from remaining road by 50 hollow cones made of recycled cardboard. Base diameter is 40 cm and height is 1 m. Find cost of painting at ₹12/m² (π=3.14, √1.04=1.02).

A hemispherical bowl made of brass has inner diameter 10.5 cm. Find cost of tin-plating on inside at ₹16 per 100 cm².

A dome of a building is in form of hemisphere. From inside, it was white-washed at cost of ₹498.96. If rate is ₹2/m², find (i) inside surface area (ii) volume of air inside.

Twenty seven solid iron spheres of radius r and surface area S are melted to form a sphere with surface area S'. Find (i) radius r' of new sphere (ii) ratio of S and S'.

Case Study Scenario: A conical heap of wheat has diameter 10.5 m and height 3 m. Question: Find its volume and canvas area needed to cover it.

Case Study Scenario: The moon's diameter is approximately one-fourth of diameter of earth. Question: Find ratio of their surface areas and volumes.

A hemispherical tank is full of water. It is emptied by a pipe at rate of 3 4/7 litres per second. How much time will it take to empty half tank if diameter is 3 m?

A capsule of medicine is in shape of a sphere of diameter 3.5 mm. How much medicine (in mm³) is needed to fill this capsule?

Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find (i) radius of base (ii) total surface area.

Surface Areas and Volumes
CBSE Most Repeated PYQs