Surface Areas and Volumes: 9 Math
NCERT Exercise 13.4: 9th math
What is a sphere? A sphere is a three dimensional object resembles a circular ball. Rather a circular ball is called a sphere. For example a ball.
Important Formula
Surface Area of a Sphere = 4 times the area of a circle of radius r `=4\ pi\ r^2`
Curved Surface Area of a Hemisphere `=2\ pi\ r^2`
Total Surface Area of a hemisphere `=3\ pi\ r^2`
Assume `pi=22/7`, unless stated otherwise.
NCERT Exercise 13.4 Questions and Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.4 Question (1) Find the surface area of a sphere of radius
(i) 10.5cm
(ii) 5.6 cm
(iii) 14 cm
Solution
(i) Surface area of a sphere of radius 10.5 cm
Given, given radius of sphere = 10.5 cm
Therefore, Surface area of given sphere = ?
We know that, Surface area of sphere = 4 ℿ r2
= 4 × `22/7` × 10.5 cm × 10.5 cm
= 4 × 22 × 1.5 cm × 10.5 cm
= 88 × 15.75 cm2
= 1386 cm2
Thus, Surface area of surface = 1386 cm2 Answer
(ii) Surface are of sphere of radius = 5.6 cm
We know that Surface area of a sphere = 4 ℿ r2
=4 × `22/7` × 5.6 cm × 5.6 cm
= 4 × 22 × 0.8 cm × 5.6 cm
= 88 × 4.48 cm2
= 394.24 cm2
Thus, Surface area of given sphere = 394.24 cm2 Answer
(iii) Surface area of sphere having radius = 14 cm
We know that Surface area of a sphere = 4 ℿ r2
Thus, Surface area of given sphere
= 4 × `22/7` × 14 cm × 14 cm
= 4 × 22 × 2 cm × 14 cm
= 88 × 28 cm2
= 2464 cm2
Thus, Surface area of given shpere = 2464 cm2 Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.4 Question (2) Find the surface area of a sphere of diameter:
(i) 14 cm
(ii) 21 cm
(iii) 3.5 m
Solution
(i) Surface area of sphere having diameter 14 cm
Given, diameter of the sphere = 14 cm
Therefore, radius (r) = 14/2 = 7 cm
We know that Surface area of a sphere = 4 ℿ r2
Therefore, Surface area of given sphere
= 4 × `22/7` × 7 cm × 7 cm
= 4 × 22 × 1 cm × 7 cm
= 88 × 7 cm2
= 616 cm2
Therefore, Surface area of given sphere = 616 cm2 Answer
(ii) Surface area of sphere having diameter = 21 cm
Therefore, Radius (r) = 21/2 cm = 10.5 cm
We know that Surface area of a sphere = 4 ℿ r2
Therefore, Surface area of given sphere
= 4 × `22/7` × 10.5 cm × 10.5 cm
= 4 × 22 × 1.5 cm × 10.5 cm
= 88 × 15.75 cm2
= 1386 cm2
Thus, Surface Area of given Sphere = 1386 cm2 Answer
(iii) Surface area of sphere having diameter = 3.5 cm
Therefore, Radius (r) = 3.5/2 = 1.75 cm
We know that Surface area of a sphere = 4 ℿ r2
Therefore, Surface area of given sphere
= 4 × `22/7` × 1.75 cm × 1.75 cm
= 4 × 22 × 0.25 cm × 1.75 cm
= 88 × 0.4375 cm2
= 38.5 cm2
Thus, Surface Area of given Sphere = 38.5 cm2 Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.4 Question (3) Find the total surface area of a hemisphere of radius 10 cm. (use ℿ= 3.14)
Solution
Given, Radius of hemisphere = 10 cm
And ℿ = 3.14
Thus, Total Surface Area of given hemisphere = ?
Now, we know that Total Surface Area of a Hemisphere `=3\ pi\ r^2`
Therefore, Total surface area of given Hemisphere
= 3 × 3.14 × (10 cm)2
= 3 × 3.14 × 100 cm2
= 3 × 314 cm2
= 942 cm2
Thus, Total Surface Area of given Hemisphere = 942 cm2 Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.4 Question (4) The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface area of the balloon in the two cases.
Solution
Given, The radius of balloon increases from 7 cm to 14 cm due to pumping of air.
Thus here there are two cases, i.e. before pumping of air and after pumping of more air.
Thus, ratio of Surface Area of balloon in given two cases = ?
Thus, in Case (i) i.e. before pumping of more air (C1)
Radius (r) =7 cm
Now we know that Surface Area of a sphere = 4 ℿ r2
Thus, Surface Area of balloon before pumping of more air i.e. in C1
= 4 × ℿ × 7 × 7 - - - - (i)
Now, in Case (ii) i.e. after pumping of more air in the balloon (C2)
Given, Radius (R) =14 cm
Therefore, Surface Area of Balloon in case (ii) i.e. C2
= 4 × ℿ × 14 × 14 - - - - (ii)
Now, ratio of balloon before pumping of air and after pumping of more air,
i.e. C1 : C2
= 4 × ℿ × 7 × 7 : 4 × ℿ × 14 × 14
`=(4\ pi\ 7xx7)/(4\ pi\ 14xx14)`
`=1/4 = 1:4`
Thus, ratio of surface area of balloon in given two cases = 1 : 4 Answer
Reference: