what is the lateral area of the cone to the nearest whole number 40 60

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The first step in finding the surface area of a cone is to mensurate the radius of the circle office of the cone. The adjacent pace is to detect the area of the circle, or base. The expanse of a circumvolve is three.fourteen times the radius squared ( πr ² ). Now, you will need to discover the expanse of the cone itself. In order to practice this, you must measure the side (camber elevation) of the cone. Make sure you utilise the aforementioned class of measurement as the radius.

Yous can now use the measurement of the side to find the area of the cone. The formula for the area of a cone is 3.14 times the radius times the side (

πrl ).

And then the surface expanse of the cone equals the expanse of the circle plus the expanse of the cone and the concluding formula is given by:

SA = πr ^two + πrl

Where,
r is the radius
h is the elevation
l is the slant meridian

The area of the curved (lateral) surface of a cone =

πrl
 Note:
A cone does not accept compatible (or congruent) cross-sections. (more about conic department here )

Example ane: A cone has a radius of 3cm and acme of 5cm, find full surface area of the cone.
Solution :
To begin with we need to find slant height of the cone, which is adamant by using Pythagoras, since the cross section is a right triangle.

l ^two = h ⁱⁱ + r ²
fifty ⁱⁱ = five ⁱⁱ + 3 ⁱⁱ
l ^two = 25 + 9
l = √(34)
l = 5.83 cm

And the total surface area of the cone is:
SA = πr ² + πrl
SA = π · r · (r + l)
SA = π · 3 · (three + 5.83)
SA = 83.17 cm ²

Therefore, the full surface area of the cone is 83.17cm ²

Example 2: The full surface area of a cone is 375 square inches. If its slant height is iv times the radius, then what is the base bore of the cone? Use π = 3.
Solution :
The full surface surface area of a cone = πrl + πr ² = 375 inch ^two
Slant acme: fifty = 4 × radius = 4r

Substitute l = 4r and π = 3
three × r × iv r + 3 × r ² = 375
12r ² + 3r ⁱⁱ = 375
15r ² = 375
r ^two = 25
r = 25
r = 5

So the base radius of the cone is 5 inch.
And the base diameter of the cone = 2 × radius = two × v = x inch.

Example 3: What is the total surface area of a cone if its radius = 4cm and superlative = 3 cm.
Solution :
As mentioned earlier the formula for the surface expanse of a cone is given by:
SA = πr ² + πrl
SA = πr(r + 50)

Every bit in the previous example the slant tin be determined using Pythagoras:
50 ² = h ⁱⁱ + r ²
l ² = three ² + iv ²
fifty ² = 9 + 16
fifty = five

Insert l = 5 we will become:
SA = πr(r + l)
SA = 3.14 · four · (4+5)
SA = 113.04 cm ²

Instance 4: The slant height of a cone is 20cm. the bore of the base of operations is 15cm. Find the curved surface expanse of cone.
Solution :
Given that,
Slant height: 50 = 20cm
Diameter: d = 15cm
Radius: r = d/ii = 15/2 = 7.5cm

Curved surface area = πrl
CSA = πrl
CSA =π · 7.5 · 20
CSA =471.24 cm ²

Case five: Elevation and radius of the cone is 5 yard and vii yard. Find the lateral surface expanse of the given cone.
Solution :
Lateral surface area of the cone = πrl

Step 1 :
Slant top of the cone:
50 ² = h ² + r ^two
l ^two = 7 ⁱⁱ + 5 ²
l ⁱⁱ = 49 + 25
50 = eight.6

Step 2 : Lateral surface area:
LSA = πrl
LSA = 3.14 × 7 × viii.6
LSA =189.03 yd ²

And then, the lateral surface area of the cone = 189.03 squared yard.

Example half dozen: A circular cone is 15 inches loftier and the radius of the base of operations is 20 inches What is the lateral surface area of the cone?

Solution:

The lateral surface surface area of cone is given past:

LSA = π × r × l
LSA =three.14 × 20 × xv
LSA = 942 inch ²

Example vii: Find the total surface area of a cone, whose base radius is 3 cm and the perpendicular height is iv cm.
Solution :
Given that:
r = three cm
h = four cm

To find the total surface expanse of the cone, nosotros need slant tiptop of the cone, instead the perpendicular elevation.
The slant height

l can exist found by using Pythagoras theorem.

l ⁱⁱ = h ⁱⁱ + r ²
l ² = three ^two + iv ²
l ² = nine + 16
l = 5

The full surface area of the cone is therefore:
SA = πr(r + l)
SA = 3.fourteen · 3 · (3+5)
SA = 75.36 cm ²

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Source: https://www.web-formulas.com/Math_Formulas/Geometry_Surface_of_Cone.aspx

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