Surface Areas and Volumes: 9 Math
NCERT Exercise 13.3: 9th math
Important Formula
Curved Surface Area of A Cone `=pi \ r\ l`
Where r = radius of base and `l` = slant height
Total Surface Area of a Cone `=pi \ r(l+r)`
NCERT Exercise 13.3 Questions and Solution and Answer
Assume `p=22/7` unless stated otherwise.
Surface Areas And Volumes Class nine Math NCERT Exercise 13.3Question (1) Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Finds its curved surface area.
Solution
Given, Diameter of the base = 10.5 cm
Therefore, Radius = 10.5/2 = 5.25 cm
And, Slant height = 10 cm
Therefore, Curved surface area of the given cone = ?
We know that, Curved Surface Area of a Cone `= pi r l`
Thus, Curved Surface Area of the given Cone of the given cone
`= 22/7 xx 5.25 xx 10\ cm^2`
= 22 × 0.75 × 10 cm2
= 22 × 7.5 cm2
= 165 cm2
Thus, Curved Surface Area of given Cone = 165 cm2 Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.3Question (2) Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Solution
Given, Slant height of the cone = 21 m
And, Base diameter of the cone = 24 m
Therefore, radius of cone (r) = 12 m
Thus, total surface area of the given cone = ?
We know that, Total surface area of a cone `= pi r (l + r)`
Thus, Total Surface Area of the given cone
`=22/7 xx 12 (21+ 12)`
`=22/7 xx 12 xx 33`
= 1244.57 m2
Thus, total surface of the given cone = 1244.57 m2 Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.3Question (3) Curved surface area of a cone is 308 cm2 and slant height is 14 cm. Find
(i) Radius of the base and
(ii) Total surface area of the cone.
Solution
Given, Curved surface area of the cone = 308 cm2
And, Slant height of the cone = 14 cm
Therefore, (i) radius of the base and (ii) Total surface area of the cone = ?
(i) Radius of the base
We know that, Curved surface area of a cone = ℿ r `l`
Thus, Curved Surface Area of given Cone
= `22/7` × r × 14
⇒ 308 = `22/7` × r × 14
⇒ 308 = 22 × r × 2
⇒ 308 = 44 r
`=>r=308/44`
⇒ r = 7 cm
Thus, radius of the base of given cone = 7 cm Answer
(ii) Total surface area of the cone
We know that, Total surface area of a cone `= pi\ r (r + l)`
Therefore, Total surface area of the given cone
= `22/7` × 7 (7 + 14)
= 22 × (7 + 14)
= 22 × 21
= 462 cm2
Thus, Total Surface Area of the given cone = 462 cm2 Answer
Surface Areas And Volumes Class nine Math NCERT Exercise 13.3Question (4) A conical tent is 10 m heigh and the radius of its base is 24 m. Find
(i) Slant height of the tent.
(ii) Cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70.
Solution
Given, Height of conical tent = 10 m
And, Base radius of the conical tent = 24 m
Therefore, (i) Slant height and (ii) Cost of canvas at the rate of Rs 70 per 1m2 = ?
(i) Slant height of the tent.
In a cone, height, radius and slant height of a cone together make a right angled triangle.
Therefore, (slant height)2 = (height)2 + (radius)2
Therefore, {slant height of the given cone(`l`)}2
= (102 )+(24)2
⇒ `l^2` = 100 + 576
⇒ `l^2 = 676`
`=>l=sqrt(676)`
⇒ `l` = 26 m
Thus, slant height of the given cone = 26 m Answer
(ii) Cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70.
Here canvas required to make the tent = Curved surface area of the given conical tent
Now, we know that, Curved Surface Area of a Cone `=pi\ r\ l`
Therefore, Curved surface area of the given tent
= `22/7` × 24 × 26 m2
=`22/7` × 624 m2
= `13728 /7` m2
Thus, Area of canvas to make the tent `=13728/7\m^2`
Calculation of cost of the canvas
As given in the question, rate of canvas = Rs 70 per square meter
Therefore, cost of canvas = Area of canvas × Rate of canvas
`= 13728/7xx 70`
= Rs 137280.00
Thus, cost of canvas to make the tent = Rs 137280.00 Answer
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