Activities 9.6 and 9.7 — Volume of Solids and Calculating Density — "The Amazing World of Solutes, Solvents, and Solutions"

1. 13 marksCuriosity Grade 8, Chapter 9, page 145

   How is the volume of a regular solid found? Work through the chapter's notebook example.

   Hint. Three measurements with a scale and one multiplication.

   The method (Activity 9.6). Collect cuboid objects — a notebook, a shoe box, a dice. Measure the length (l), width (w), and height (h) of the objects using a scale.

   Volume = l × w × h

   The chapter's example. Suppose the length of the notebook is 25 cm, the width is 18 cm, and the height is 2 cm.

   Volume = 25 cm × 18 cm × 2 cm = 900 cm³

   ✦ Watch the units as you multiply, since they are part of the answer. Three lengths in centimetres give a volume in cm³, which is where the cube comes from. Because the units multiply along with the numbers, measuring one side in millimetres and the others in centimetres would give a meaningless result — all three must be in the same unit before you begin.

   Why this method needs a regular shape. The formula assumes the object really is a cuboid, with flat faces and square corners. A stone has no length, width or height to measure, which is precisely the problem Activity 9.7 exists to solve.

2. 24 marksCuriosity Grade 8, Chapter 9, page 146

   Describe Activity 9.7 — finding the volume of an irregular solid such as a stone. Work through the chapter's numbers.

   Hint. The stone cannot be measured with a scale, so measure what it pushes out of the way instead.

   The procedure.

   1. Fill a measuring cylinder with water to any desired volume — say 50 mL — and record this as the initial volume (A).
   2. Tie the object with a thread and slowly lower it into the cylinder.
   3. Record the final volume (B) after the level rises — say 55 mL.
   4. Subtract the initial volume from the final volume ... This is the volume of the object.

   Volume of the stone = B − A = 55 mL − 50 mL = 5 mL = 5 cm³

   Table 9.2 records exactly these four columns — initial volume (A), final volume (B), volume of water displaced (B − A), and volume of the object in cm³.

   ✦ The idea is that the stone and the water it pushed aside occupy the same space. You cannot measure the stone, but you can measure the water — and since the water level rose by exactly the volume the stone now takes up, the rise is the stone's volume. The unit change from mL to cm³ is a relabelling, not a calculation, because 1 mL = 1 cm³.

   Why a thread, and why slowly? The thread lets you lower and retrieve the stone without dipping your fingers in — which would displace water too and inflate the reading. Lowering it slowly avoids a splash that would carry water out of the cylinder and make the final reading too low.

3. 34 marksCuriosity Grade 8, Chapter 9, page 146

   Calculate the density of the stone using the measurements from Activities 9.3 and 9.7.

   Hint. You measured the mass in one activity and the volume in another; now put them together.

   The two measurements.

   Quantity	Where it came from	Value
   Mass	Activity 9.3, digital balance	16.400 g
   Volume	Activity 9.7, displacement	5 cm³

   The calculation.

   Density = Mass ÷ Volume = 16.400 g ÷ 5 cm³ = 3.28 g/cm³

   ✦ This is the point the whole middle of the chapter has been building to. Density cannot be measured directly — there is no density meter. It is calculated from two separate measurements, each made with its own instrument and its own precautions. Because the answer depends on both, an error in either one carries straight through: a stone weighed while still wet, or a level misread from above, gives a wrong density even if the arithmetic is perfect.

   Compare with water. 3.28 g/cm³ against about 1 g/cm³ — the stone is a little over three times as dense as water, so its relative density is 3.28, and it sinks.

   (Note the units: grams divided by cubic centimetres gives g/cm³. The unit falls out of the formula and never has to be remembered separately.)

4. 43 marksCuriosity Grade 8, Chapter 9, page 146

   Why can the volume in mL be written as cm³ for solids? Would this work for any pair of units?

   Hint. One is a genuine equality; not every unit swap is.

   Because the two units are equal in size. A commonly used submultiple of a litre is millilitre (mL) which is equivalent to 1 cm³. So 5 mL and 5 cm³ are the same quantity written two ways, and the chapter's note simply says so: the values of volume are obtained in units of mL, which can be written in the equivalent unit cm³ for solids.

   No, this does not work for any pair. It works here only because 1 mL happens to be defined as exactly 1 cm³. Going from mL to litres, or cm³ to m³, requires real conversion:

   Change	What it needs
   mL → cm³	Nothing — relabel
   mL → L	Divide by 1000
   cm³ → m³	Divide by 1 000 000

   ✦ Why the chapter bothers to point it out. Liquids are conventionally measured in mL and solids described in cm³, so a displacement measurement crosses that convention — you read a liquid scale to find a solid's volume. Without the note, a student might reasonably think a conversion had been skipped. Since none is needed, none is done, and saying so removes the doubt.

5. 53 marksCuriosity Grade 8, Chapter 9, page 146

   A student drops the stone into the cylinder rather than lowering it on a thread, and some water splashes out. What happens to the calculated density, and in which direction is the error?

   Hint. Work out which measurement is wrong and which way it is wrong.

   What goes wrong. Water leaves the cylinder, so the final level B is lower than it should be. The calculated volume B − A therefore comes out too small.

   The effect on the density. Density = Mass ÷ Volume, and the mass is unaffected. Since a smaller number is being divided into the same mass, the calculated density comes out too large.

   With the correct volume: 16.400 ÷ 5 = 3.28 g/cm³ If 1 mL splashed out: 16.400 ÷ 4 = 4.1 g/cm³ — an error of a quarter

   ✦ Being able to say which way an error pushes the answer is worth as much as spotting it. A student who says only 'the reading would be wrong' has noticed the problem; one who says 'the volume would be underestimated, so the density would be overestimated' has understood it. Because every step of the calculation is a division or a subtraction with a known direction, the direction of the error can always be traced.

   Two more errors worth naming, with their directions. Dipping your fingers in raises the level, giving too large a volume and too small a density. Weighing the stone while still wet gives too large a mass and too large a density.

6. 63 marksCuriosity Grade 8, Chapter 9, page 147

   What does the chapter say about the density of the Earth's layers, and what causes the pattern?

   Hint. Read the 'Let us dig deeper' box, and note the two things that rise together with depth.

   Our planet, Earth, is composed of several layers, such as crust, upper mantle, lower mantle, outer core, and inner core, each with its particular range of density. The outermost layer, called the crust, is the lightest and the density of the different layers increases as we move towards the centre. As one moves deeper into the Earth, both the pressure and the temperature rise significantly, making the materials heavier and more compact.

   Layer, outward to inward	Density
   Crust	Lightest
   Upper mantle	↓ increasing
   Lower mantle	↓
   Outer core (liquid)	↓
   Inner core (solid)	Greatest

   ✦ The box connects directly to section 9.5.3, two pages later. For gases, increasing pressure causes the particles to move closer together. As a result, the volume of the gas decreases and its density increases. The same compression happens to rock under the enormous pressures at depth — so the pattern of increasing density is not a coincidence about which materials happen to be where, but partly a consequence of the pressure they are under.

   Note that temperature and pressure rise together here, and they push density opposite ways — heating lowers density, pressure raises it. The chapter says the net result is heavier and more compact material, so pressure wins at these depths.

Solutions written by the tuition.in editorial team and checked against NCERT Curiosity — Textbook of Science for Grade 8, Chapter 9 (hecu109.pdf), Reprint 2026-27, pages 134-151. Questions are referenced from the NCERT textbook for identification.