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Chapter 10: Surface Areas and Volumes

    Introduction

    Surface Area of Cuboid

    Right Circular Cylinder

    Right Circular Cone

    Sphere

    Exercise 10.1

    Exercise 10.2

    Exercise 10.3

    Exercise 10.4

    What We Have Discussed

    What We Have Discussed

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 10: Surface Areas and Volumes > Right Circular Cylinder

Right Circular Cylinder

Most of the real life examples of a cylinder we see day to day are right circular cylinders. For example: a can, cylinderical pillars, tube lights, pipes etc. When we try to draw a net for such cylinders, we get:

1. Top and base faces are circles of radius "r"

2. The curved(lateral) surface, upon being cut along the vertical length, giving a rectangle of length "2πr" and breadth of "h"

Flower Can

Cold drink can

Cylinder Net

Find Curved surface area of the following cylinders:

(i) r = 14 cm, h = 8 cm

(ii) d = 2 m , h = 2 m

Instructions

(i) r = 14cm , h = 8cm
Curved Surface Area = 2πrh = 2 × 3.1416 × × = π ≈ cm2
(ii) d = 2m, h = 2m
r = d2 = 22 = m
Curved Surface Area = 2πrh = 2 × 3.1416 × × = π ≈ m2

Instructions

Observe the above given figure

  • We can see that: Surface Area of Cylinder = × Top/Base Circle + Lateral surface
  • Thus, Surface Area of Cylinder = 2 × + where r and h are radius and height of the cylinder.
  • Simplifying, we get: Surface Area of Cylinder = 2πr(r + h)
  • We have found the surface area formula for a cylinder.

Thus,

Volume of cylinder = area of base × height = πr2 x h = πr2h

A company sells biscuits. For packing purpose they are using cuboidal boxes:

(1) Box A = 3 cm × 8 cm × 20 cm

(2) Box B = 4 cm × 12 cm × 10 cm

What size of the box will be economical for the company?

Instructions

Which is more economical ?

  • First, let's calculate the volume of both the boxes.
  • Volume(Box A) = cm3 while Volume(Box B) = cm3
  • We see that both are equal.
  • In order to check which box is more economical, we can check the material used for packaging i.e. we need to calculate the of the boxes. Also
  • Surface area of a box of length l, breadth b and height h =
  • Thus, Surface area for A = Material needed for box A = cm2
  • Surface area for B = Material needed for box B = cm2
  • Thus, is more economical as it will be using lesser amount of material.
  • Thus, Box B is more economical for the manufacturers.