CLASS 10 · CHAPTER 12

Surface Areas and Volumes
Practice Questions

20 curated NCERT & Board Exam questions to test your understanding. Click on "Show Solution & Answer" to check step-by-step working.

20Questions

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Q1MCQ1 Mark

2 cubes each of volume 64 cm³ are joined end to end. Surface area of resulting cuboid is:

Q2MCQ1 Mark

A wooden toy rocket is in shape of cone mounted on cylinder. Total height is 26 cm, cone height is 6 cm. Cone slant height (r=2.5cm) is:

Q3MCQ1 Mark

Curved surface area of hemisphere of radius r is:

Q4MCQ1 Mark

Ratio of volumes of two spheres is 64 : 27. Ratio of their surface areas is:

Q5Assertion-Reason1 Mark

Assertion (A): Total surface area of solid hemisphere of radius r is 3πr². Reason (R): Total surface area includes curved surface 2πr² plus flat base area πr².

Q6Assertion-Reason1 Mark

Assertion (A): When a sphere is melted and remolded into a cone, its total volume remains unchanged. Reason (R): Law of conservation of volume states volume is conserved during reshaping.

Q7Short Answer2 Marks

A vessel is in form of hollow hemisphere mounted by hollow cylinder. Diameter is 14 cm, total height is 13 cm. Find inner surface area.

Q8Short Answer2 Marks

A toy is in form of cone of radius 3.5 cm mounted on hemisphere of same radius. Total height is 15.5 cm. Find total surface area.

Q9Short Answer2 Marks

A medicine capsule is in shape of cylinder with two hemispheres stuck to ends. Length is 14 mm, diameter is 5 mm. Find surface area.

Q10Short Answer2 Marks

A solid wooden toy consists of hemisphere surmounted by cone of height 2cm and base diameter 4cm. Find toy volume.

Q11Short Answer2 Marks

A solid iron pole consists of cylinder of height 220 cm and diameter 24 cm surmounted by cylinder of height 60 cm and radius 8 cm. Find mass (1 cm³ = 8g).

Q12Long Answer3 Marks

A gulab jamun contains sugar syrup up to about 30% of its volume. Find syrup in 45 gulab jamuns shaped like cylinder with 2 hemispherical ends (l=5cm, d=2.8cm).

Q13Long Answer3 Marks

A pen stand made of wood is in shape of cuboid with 4 conical depressions to hold pens. Cuboid: 15cm×10cm×3.5cm. Depression: r=0.5cm, depth=1.4cm. Find wood volume.

Q14Long Answer3 Marks

A spherical glass vessel has cylindrical neck 8 cm long, 2 cm in diameter; diameter of spherical part is 8.5 cm. Find its volume.

Q15Long Answer3 Marks

A tent is in shape of cylinder surmounted by conical top. Height and diameter of cylindrical part are 2.1 m and 4 m, slant height of top is 2.8 m. Find canvas area & cost at ₹500/m².

Q16Case Study4 Marks

Case Study Scenario: A boiler is made in form of cylinder with 2 hemispherical ends. Diameter is 2 m and total length is 7 m. Question: Find total capacity (volume) and total surface area of boiler.

Q17Case Study4 Marks

Case Study Scenario: An ice-cream cone consists of cone filled with ice-cream having hemispherical top. Radius is 3 cm and height of cone is 12 cm. Question: Find total volume of ice-cream.

Q18PYQ5 Marks

A solid toy in form of hemisphere surmounted by right circular cone. Height of cone is 2cm and diameter of base is 4cm. If right circular cylinder circumscribes toy, find difference of volumes.

Q19PYQ5 Marks

A copper rod of diameter 1 cm and length 8 cm is drawn into wire of length 18 m of uniform thickness. Find thickness of wire.

Q20PYQ5 Marks

Water in canal 6 m wide and 1.5 m deep is flowing with speed of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is needed?

Surface Areas and Volumes Practice Questions