Surface Areas and VolumesIntroduction

Every morning at six, a milk tanker pulls into the dairy in Riya's village. Riya has seen it a hundred times, but today her uncle, who runs the dairy, asks her two questions about its big steel tank. How many litres of milk can it carry? And how much paint will he need to give it a fresh coat before the monsoon?

The first question is about the tank's volume, the second about its surface area. In Class IX you learnt to find both for the basic solids in Fig. 12.1: the cuboid, the cone, the cylinder and the sphere.

Fig. 12.1 — the four basic solids. In every figure of this chapter, cylinders are blue, cones orange, spheres and hemispheres green, and cubes and cuboids purple.

But is the tank one of these four? Take a good look at it in Fig. 12.2.

Fig. 12.2 — a tanker carrying milk from the dairy.

The tank is not a single basic solid — but it is built from them. Its long middle is a cylinderconesphere, and each rounded end is a hemisphere, so it has twoonethree hemispheres in all.

The Shape Workshop

Riya's uncle also has a small workshop that makes wooden models for the village school. Three orders have just come in, and every one of them can be made from the solids on the shelf.

Build all three orders. Tap pieces to put them on the bench, then press Assemble. An order needs exactly the right pieces — no more and no fewer.

Three new shapes, and not one new kind of piece. That is the idea behind this whole chapter. An object made by joining basic solids — a combination of solids — can be measured piece by piece, using only the formulas you already know.

Solids Hiding Everywhere

So how would you find the surface area, the volume or the capacity of objects like these? None of the Class IX formulas fits them directly. In this chapter you will find out — by doing exactly what you did in the workshop: break the object into basic solids, and measure the pieces.