Identify the lateral area and surface area of a right cone with radius 7 cm and slant height 15 cm a. L = 329.9 cm2; S = 373.9 cm2 b. L = 329.9 cm2; S = 483.8 cm2 c. L = 659.7 cm2; S = 483.8 cm2 d. L = 659.7 cm2; S = 813.6 cm2

Step-by-step explanation:

Step-by-step explanation:

a.

L

=

329.9

c

m

2

;

S

=

373.9

c

m

2

.

b.

L

=

659.7

c

m

2

;

S

=

483.8

c

m

2

.

c.

L

=

659.7

c

m

2

;

S

=

813.6

c

m

2

.

d.

L

=

329.9

c

m

2

;

S

=

483.8

c

m

2

.

Surface Area of a Cone:

In the three dimensional geometry, a cone is a shape that has a circular base and a lateral surface is associated with a vertex and the base.

The height of the cone is the length of a line segment that joins the base to the vertex of the cone.

The radius of the cone is the same as the radius of the base.

Surface area of a cone

(a) Lateral Surface Area

If

l

and

r

are the slant height and radius of a cone then its lateral surface area is given by the formula-

L

=

π

r

l

where

L

is the lateral surface area of the cone

(b) Total surface area

It is the sum of the area of the circular base and the lateral surface area of the cone.

S

=

L

+

π

r

2

S

=

π

r

l

+

π

r

2

Where

S

is the total surface area of the cone

Answer and Explanation:

Given that the radius and slant height of a right cone is

7

c

m

and

15

c

m

respectively

r

=

7

c

m

l

=

15

c

m

So the lateral surface area of the cone-

L

=

π

r

l

L

=

π

(

7

)

(

15

)

L

=

105

π

L

=

105

(

3.14159

)

L

=

329.866

L

≈

329.9

c

m

2

And the total surface area of the cone-

S

=

L

+

π

r

2

S

=

329.9

+

π

(

7

)

2

S

=

329.9

+

49

(

3.14159

)

S

=

329.9

+

153.937

S

=

483.83

c

m

2

So the lateral area and total area of a right cone are

329.9

c

m

2

and

483.8

c

m

2

respectively.

Step-by-step explanation:

a.

L

=

329.9

c

m

2

;

S

=

373.9

c

m

2

.

b.

L

=

659.7

c

m

2

;

S

=

483.8

c

m

2

.

c.

L

=

659.7

c

m

2

;

S

=

813.6

c

m

2

.

d.

L

=

329.9

c

m

2

;

S

=

483.8

c

m

2

.

Surface Area of a Cone:

In the three dimensional geometry, a cone is a shape that has a circular base and a lateral surface is associated with a vertex and the base.

The height of the cone is the length of a line segment that joins the base to the vertex of the cone.

The radius of the cone is the same as the radius of the base.

Surface area of a cone

(a) Lateral Surface Area

If

l

and

r

are the slant height and radius of a cone then its lateral surface area is given by the formula-

L

=

π

r

l

where

L

is the lateral surface area of the cone

(b) Total surface area

It is the sum of the area of the circular base and the lateral surface area of the cone.

S

=

L

+

π

r

2

S

=

π

r

l

+

π

r

2

Where

S

is the total surface area of the cone

Answer and Explanation:

Given that the radius and slant height of a right cone is

7

c

m

and

15

c

m

respectively

r

=

7

c

m

l

=

15

c

m

So the lateral surface area of the cone-

L

=

π

r

l

L

=

π

(

7

)

(

15

)

L

=

105

π

L

=

105

(

3.14159

)

L

=

329.866

L

≈

329.9

c

m

2

And the total surface area of the cone-

S

=

L

+

π

r

2

S

=

329.9

+

π

(

7

)

2

S

=

329.9

+

49

(

3.14159

)

S

=

329.9

+

153.937

S

=

483.83

c

m

2

So the lateral area and total area of a right cone are

329.9

c

m

2

and

483.8

c

m

2

respectively.