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Class 9 Maths: Math of Space, Surface Area and Volume, 8 practice questions with answers

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These are 8 practice questions on Chapter 14, Math of Space: Surface Area and Volume, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part II (First Edition, August 2026). Each has a worked answer and the textbook page it comes from. They cover the surface area and volume of a cuboid, the capacity of a tank in litres, the surface areas of a closed cylinder and a tumbler, the slant height and surface area of a cone, why a cone holds one third of a cylinder, and the surface area and volume of a sphere and a hemisphere. Answers are left in terms of π, so no approximation for π is needed. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Manjari, Grade 9, Part II, Chapter 14, printed pages 123 to 148):

Cuboids

Question 1. A cardboard box is a cuboid 47 cm long, 36 cm wide and 29 cm high. Find its total surface area and its volume.

Answer: total surface area 8198 cm²; volume 49068 cm³. TSA = 2(lw + wh + hl) = 2(47 × 36 + 36 × 29 + 29 × 47) = 2(1692 + 1044 + 1363) = 2 × 4099 = 8198 cm². Volume = 47 × 36 × 29 = 49068 cm³. (Cuboid, pages 123 and 124.)

Question 2. The inside of a water tank is a cuboid 185 cm long, 96 cm wide and 84 cm deep. How many litres of water can it hold when full?

Answer: 1491.84 litres. Volume = 185 × 96 × 84 = 17760 × 84 = 1491840 cm³. Since 1000 cm³ = 1 litre, the tank holds 1491840 ÷ 1000 = 1491.84 litres. (Volume of a cuboid, page 124; litres, page 141.)

Cylinders and cones

Question 3. A closed cylindrical tin has radius 28 cm and height 53 cm. Find its curved surface area and its total surface area, in terms of π.

Answer: curved surface area 2968π cm²; total surface area 4536π cm². CSA = 2πrh = 2π × 28 × 53 = 2968π cm². TSA = 2πr(h + r) = 2π × 28 × (53 + 28) = 56π × 81 = 4536π cm². (Cylinder, page 128.)

Question 4. A tumbler is a cylinder closed at the bottom and open at the top, with radius 34 mm and height 77 mm. Find the area of its outer surface and its volume, in terms of π.

Answer: surface area 6392π mm²; volume 89012π mm³. For a cylinder closed at one end, surface area = πr(2h + r) = π × 34 × (154 + 34) = 34π × 188 = 6392π mm². Volume = πr²h = π × 1156 × 77 = 89012π mm³. (Cylinder closed at one end, and volume, page 128.)

Question 5. A cone has base radius 36 cm and height 77 cm. Find its slant height, its curved surface area and its total surface area.

Answer: slant height 85 cm; curved surface area 3060π cm²; total surface area 4356π cm². l² = h² + r² = 77² + 36² = 5929 + 1296 = 7225, so l = 85 cm (85 × 85 = 7225). CSA = πrl = π × 36 × 85 = 3060π cm². TSA = πrl + πr² = πr(l + r) = π × 36 × 121 = 4356π cm². (Slant height, page 130; surface area of a cone, page 131.)

Question 6. Find the volume of the cone in Question 5, and the volume of a cylinder with the same base radius and the same height. How many conefuls of water fill the cylinder?

Answer: cone 33264π cm³; cylinder 99792π cm³; 3 conefuls. Cone: (1/3)πr²h = (1/3)π × 1296 × 77 = (1/3) × 99792π = 33264π cm³. Cylinder: πr²h = π × 1296 × 77 = 99792π cm³. Since 99792π ÷ 33264π = 3, the cylinder holds exactly three conefuls, as in the chapter's salt and clay experiments. (Volume of a cone, pages 132 and 133.)

Spheres and hemispheres

Question 7. A globe is a sphere of radius 42 cm. Find its surface area and its volume, in terms of π.

Answer: surface area 7056π cm²; volume 98784π cm³. Surface area = 4πr² = 4π × 1764 = 7056π cm². Volume = (4/3)πr³ = (4/3)π × 74088 = 98784π cm³. (Sphere, pages 136 and 137.)

Question 8. A solid hemisphere, like half of a wooden ball, has radius 39 cm. Find its curved surface area, its total surface area (including the flat circular face) and its volume, in terms of π.

Answer: curved surface area 3042π cm²; total surface area 4563π cm²; volume 39546π cm³. r² = 1521. CSA = 2πr² = 3042π cm². TSA = 3πr² = 4563π cm². Volume = (2/3)πr³ = (2/3)π × 59319 = 39546π cm³. (Hemisphere, page 140.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 122.

The formulas are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.