1 Mark
CBSE BOARD PYQS · CHAPTER 12
Surface Areas and Volumes
CBSE Most Repeated PYQs
Solve official CBSE Previous Year Board Questions (2015-2024) for Surface Areas and Volumes. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.
1 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:
1 Mark
Curved surface area of hemisphere of radius r is:
1 Mark
Ratio of volumes of two spheres is 64 : 27. Ratio of their surface areas is:
1 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.
1 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.
2 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.
2 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.
2 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.
2 Marks
A solid wooden toy consists of hemisphere surmounted by cone of height 2cm and base diameter 4cm. Find toy volume.
2 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).
3 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).
3 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.
3 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.
3 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.
4 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.
4 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.
5 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.
5 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.
5 Marks