Lateral Surface Area of Cone

Concept Explanation

Lateral Surface Area of Cone

Lateral Surface Area of Cone: The curved surface area of a cone is also called the lateral surface area. Lateral surface area of cone $=pi rl$

where r = radius of the base of the cone and l = slant height of the cone and $large l=sqrt{r^2+h^2}$

Illustration: The circumference of the base of a 10m height conical tent is 44m. Calculate the length of canvas used in making the tent if width of canvas is 2m.

Solution: Given: Circumference of cone = 44 m and h =10m and breadth = 2 m

So, we have, $large 2pi r$ = 44m ..............(i)

So, Using equation (i), we have

$large 2times frac{22}{7}times r=44$

$frac{44}{7}times r=44$

$r=44times frac{7}{44}$

$r=7;m$

As we know Area of Canvas = Curved Surface Area of Cone

Area of Canvas = length x breadth = length x 2 ...................(ii) [As breadth = 2 m]

$large therefore; l=sqrt{r^2+h^2}=sqrt{49+100}=sqrt{149}m$ = 12.2 m

$large Lateral ;surface;area=pi rl=frac{22}{7}times 7times sqrt{149}m^2=268.4m^2$

Now, using equation (ii), we have

Area of Canvas = length x 2

length $=frac{area ;of; canvas}{2}$

Length of canvas = $large frac{268.4}{2}=134.2m$

Illustration: The radius and slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 sq cm, find its radius. (Use $large pi =frac{22}{7}$ )

Solution: Let r cm be the radius and l cm the slant height of the cone. Then,

r : l = 4 : 7

Let the common factor = x

$large therefore r= 4x$ cm and $large l= 7x$ cm ........................(i)

Now, curved surface area = 792 sq cm

$large pi rl =792$

$large frac{22}{7}times 4xtimes 7x=792$

$large x^{2}=frac{792}{88}$

$large x^{2}=9$

$large x=pm 3$

But x = - 3 is not possible.

Hence, x = 3

Using x = 3 in equation (i), we have

$large r= 4x=4(3)$

$large r=12$ cm

Hence radius of the base of the cone is 12 cm.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.
A. 3945 sq cm	B. 3960 sq cm	C. 3950 sq cm	D. 3970 sq cm
Right Option : B
View Explanation

Question : 2

The area of the curved surface of a cone is 60 $pi$ $cm^{2}$ . If the slant height of the cone be 8 cm, find the radius of the base.
A. 7.5	B. 6.5	C. 7.3	D. 7.2
Right Option : B
View Explanation

Question : 3

The radius of the cone is 3 cm and vertical height is 4 cm. Find the area of the curved surface.
A. 47.14 sq cm	B. 47.17 sq cm	C. 47.16 sq cm	D. 47.15 sq cm
Right Option : A
View Explanation

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