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Q: What is the surface area of a right cone with a radius of 4 and a slant height of 13?

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Total surface area = (piradius2)+(piradius*slant length)

Total surface area: (pi*36)+(pi*6*12) = 339.292 square units rounded to 3 decimal places. That is assuming that you meant the slant length and not the slant height because otherwise you would need to use Pythagoras' theorem to find the slant length.

Entire surface area of a cone: pi*radius^2 plus pi*radius*slant length

If you visualize the cone by cutting it vertically (with a plane perpendicular to the base), you can construct a right triangle to represent the radius, altitude, and slant height. This triangle has legs of 7 (the radius) and 19 (the altitude). Its hypotenuse represents the slant height. We can then use the Pythagorean theorem to solve for the slant height: 72 + 192 = s2 72 + 192 = s2 410 = s2 s = √(410) s ≈ 20.24 Therefore the cone has a slant height of √(410), or approximately 20.248456731316586933246902289901 units.

The lateral surface area is 18.85 square inches.

Related questions

The surface area of a right cone with a radius of 8 and a slant height of 15 is: 377 units squared.

These dimensions are not possible for a right cone. The radius must be less than the slant height. If we reverse the dimensions (radius 6, slant height 9) the total surface area will be about 282.74 units2

A right cone with a slant height of 6 and a radius of 7 has a total surface area of about 245.04 square units.

Surface Area = Pi*radius(radius + slant height)

The lateral surface area of a right circular cone with a radius of 12cm and a slant height of 20cm is approximately 754cm2

The surface area is a function of the height (or slant height) and the radius of the base. So, the slant height is a function of the surface area and the base-radius. Since the latter is unknown, the slant height cannot be calculated.

75.4 units2

Uisng the lateral area and tha radius, you should be able to find the height of the cone. Using the height and radius as the legs of a right triangle, use the Pythagorean Theorem. The hypotenuse is the slant height.

A right circular cone with 8 height and 6 radius has a slant height of 10.

A cone with a slant height of 22cm and radius of 7cm has a total surface area of about 637.74cm2

417.83 units squared

Slant height is 7.81 inches.

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