CLASS 09 · CHAPTER 11

Surface Areas and Volumes
Practice Questions

20 curated NCERT questions to test your problem-solving skills. Click on "Show Solution & Answer" to check step-by-step working.

20Questions

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Q1MCQ1 Mark

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

Q2MCQ1 Mark

Surface area of a sphere of radius r is:

Q3MCQ1 Mark

Volume of a sphere of radius r is:

Q4MCQ1 Mark

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

Q5Assertion-Reason1 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.

Q6Assertion-Reason1 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.

Q7Short Answer2 Marks

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

Q8Short Answer2 Marks

Find surface area of a sphere of radius 7 cm.

Q9Short Answer2 Marks

Find volume of a sphere whose radius is 3.5 cm.

Q10Short Answer2 Marks

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

Q11Short Answer2 Marks

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

Q12Long Answer3 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).

Q13Long Answer3 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.

Q14Long Answer3 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.

Q15Long Answer3 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'.

Q16Case Study4 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.

Q17Case Study4 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.

Q18PYQ5 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?

Q19PYQ5 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?

Q20PYQ5 Marks

Surface Areas and Volumes Practice Questions