01 · CBSE BOARD EXAM 2024
CBSE 2024 Board Practice Questions
CBSE 2024 · 1 MARK
Q1. 2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.
CBSE 2024 · 1 MARK
Q2. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. (Use π = 3.14)
CBSE 2024 · 2 MARKS
Q3. A vessel is in the form of a hollow hemisphere surmounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
CBSE 2024 · 3 MARKS
Q4. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
CBSE 2024 · 5 MARKS
Q5. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 3.5 cm and the total height of the toy is 15.5 cm, find the total surface area and volume of the toy.
02 · CBSE BOARD EXAM 2023
CBSE 2023 Board Practice Questions
CBSE 2023 · 1 MARK
Q6. If the radius of the base of a right circular cylinder is halved, keeping the height same, the ratio of the volume of the reduced cylinder to that of original cylinder is:
(A) 2 : 1 (B) 1 : 2 (C) 1 : 4 (D) 4 : 1
CBSE 2023 · 2 MARKS
Q7. A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent.
CBSE 2023 · 3 MARKS
Q8. A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm.
CBSE 2023 · 5 MARKS
Q9. A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm³ of iron has approximately 8 g mass. (Use π = 3.14)
03 · CBSE BOARD EXAM 2022
CBSE 2022 Board Practice Questions
CBSE 2022 · 1 MARK
Q10. Ratio of volumes of two spheres is 64 : 27. The ratio of their surface areas is:
(A) 3 : 4 (B) 4 : 3 (C) 9 : 16 (D) 16 : 9
CBSE 2022 · 2 MARKS
Q11. Find the volume of a sphere whose surface area is 154 cm².
CBSE 2022 · 3 MARKS
Q12. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
04 · CBSE BOARD EXAM 2021
CBSE 2021 Board Practice Questions
CBSE 2021 · 1 MARK
Q13. Total surface area of a solid hemisphere of radius r is:
(A) πr² (B) 2πr² (C) 3πr² (D) 4πr²
CBSE 2021 · 2 MARKS
Q14. A solid cylinder of radius 7 cm and height 10 cm is melted and recast into small spheres of radius 3.5 cm. Find the number of spheres formed.
CBSE 2021 · 3 MARKS
Q15. A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and depth is 1.4 cm. Find the volume of wood in the entire stand.
05 · CBSE BOARD EXAM 2020
CBSE 2020 Board Practice Questions
CBSE 2020 · 1 MARK
Q16. Curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.
CBSE 2020 · 3 MARKS
Q17. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.
CBSE 2020 · 5 MARKS
Q18. A juice seller was serving his customers using glasses. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π = 3.14)
06 · SELF-PRACTICE TIPS
Tips for Solving Board PYQs
01
For combined surface areas, add the exposed CSAs of individual components (do NOT add base areas!).
02
For combined volumes, simply add or subtract individual component volumes directly.
03
For cone slant height $l$, always calculate l = √(r² + h²) before finding CSA ($\pi r l$).