Project: Find the volume of your house making necessary approximations. Present how you solved it.
Step-by-step solution
Idea: Break the house into cuboids (rooms), measure the length and width of each floor and the ceiling height, find each volume and add.
- Plan: treat each room as a cuboid; measure floor length and width (paces or a tape) and the ceiling height; ignore wall thickness, cupboards and small alcoves.1 mark
- Measurements (sample): living room 5 m × 4 m = 20 m2; bedroom 1: 4 m × 3.5 m = 14 m2; bedroom 2: 3.5 m × 3 m = 10.5 m2; kitchen 3 m × 2.5 m = 7.5 m2; two bathrooms 2 m × 1.5 m = 3 m2 each; passage 4 m × 1 m = 4 m2.1 mark
- Total floor area = 20 + 14 + 10.5 + 7.5 + 6 + 4 = 62 m2. All rooms are 3 m high.1 mark
- Volume ≈ 62 × 3 = 186 m3 = 1,86,000 litres. (A house with sloping roofs or two storeys is done the same way, floor by floor, with prisms for roofs.)1 mark
Check: Rough check: a 2-bedroom flat of about 700 ft2 (≈ 65 m2) with 10 ft (≈ 3 m) ceilings has about 195 m3, close to 186 m3 ✓.
Answer to write in the exam
Each room ≈ cuboid; height = 3 m
Floor areas: 20 + 14 + 10.5 + 7.5 + 6 + 4 = 62 m2
Volume = 62 × 3 = 186 m3
∴ Volume of house ≈ 186 m3
Common mistakes that cost marks
- Adding room volumes but forgetting a room (passage, store, balcony if enclosed).
- Mixing feet and metres between rooms.
- Multiplying total floor area by the height of only one room when heights differ.
How this can come in the exam
A hall is 12 m long, 8 m wide and 4 m high. Each person needs 4 m3 of air.
(i) Find the volume of the hall. (ii) How many people can it hold? (iii) Find the area of the four walls. (iv) Painting walls costs ₹ 25 per m2; find the cost of painting the walls.
Show answer
(i) 12 × 8 × 4 = 384 m3 (1 mark). (ii) 384 ÷ 4 = 96 people (1 mark). (iii) 2(12 + 8) × 4 = 160 m2 (1 mark). (iv) 160 × 25 = ₹ 4000 (1 mark).Try one yourself
A room is 5 m × 4 m × 3 m. An air conditioner is rated for 50 m3. Is one enough?
Show answer
Volume = 60 m3 > 50 m3, so no; a bigger one is needed.
More questions like this
- What is the total surface area of a cuboid? You may refer to the net of the cuboid given in the figure.
- Compare the formula for the volume of a cuboid with the formula for the area of a rectangle (length × width).
- Try to work out for yourself why this model explains the formula for the volume of a cuboid, i.e.,
volume = area of base × height.
Write the formula for the surface area and the volume of a cube. - Observe how these two formulas are special cases of the formulas 2(wl + hl + hw) and whl, when w = h = l.
- Two solid objects are made from the same material: Cube A has side 6 cm and Cuboid B has dimensions 9 cm × 6 cm × 4 cm. Compare their volumes and surface areas and determine which object has a greater surface area. How is this useful in a real-life situation?