Mensuration — Part 1: Cylinder, cone, sphere and hemisphere: visual lesson, ICSE Class 10 Mathematics

Lesson

Cylinder, cone and sphere

Tins, funnels and footballs are all solids. In this part we find how much surface they have and how much they hold, using $\pi = \dfrac{22}{7}$ where the question says so.

In this lesson you will

Find the curved and total surface area and the volume of a solid or hollow cylinder
Find the slant height, surface areas and volume of a cone
Find the surface area and volume of a sphere, a hemisphere and a spherical shell
Choose the right formula and give the answer in square or cubic units

A cylinder: radius $r$, height $h$ (not to scale).

Concept

What you will be able to do

Use the formulas for a cylinder, solid or hollow
Find the slant height and the areas and volume of a cone
Use the formulas for a sphere, a hemisphere and a shell
Write answers in square or cubic units

The formulas of this chapter on one card.
Solid	Curved surface	Total surface	Volume
Cylinder	$2\pi r h$	$2\pi r(r + h)$	$\pi r^2 h$
Cone	$\pi r l$	$\pi r(r + l)$	$\dfrac{1}{3}\pi r^2 h$
Sphere	$4\pi r^2$ (all curved)	$4\pi r^2$	$\dfrac{4}{3}\pi r^3$
Hemisphere	$2\pi r^2$	$3\pi r^2$	$\dfrac{2}{3}\pi r^3$

Concept

The cylinder and its curved surface

A right circular cylinder has two equal circular ends and a curved surface. Cut the curved surface along a line and unroll it: it becomes a rectangle whose length is the circumference $2\pi r$ and whose width is the height $h$ .

curved surface area $= 2\pi r \times h$
the two ends add $2 \times \pi r^2$

The curved surface unrolls into a rectangle $2\pi r$ by $h$ (not to scale).

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