Best Answer

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.

Q: What is the slant height of a cone with a radius of 7 and a altitude of 19?

Write your answer...

Submit

Still have questions?

Continue Learning about Geometry

A right cone with a radius of 4 and a slant height of 13 has a total surface area of about 213.63 units2

Label t radius 6cm the height 8cm and the slant height 10cm

The perpendicular height is 6 inches and the slant height is 6.7082 inches.

5.07 inches

The volume of this cone is 15,400 cm3

Related questions

On the off chance that the question refers to a right cone, l2 = r2 + h2 by Pythagoras, where l is the slant height, h the altitude and r the radius.

A cone is a solid composed of a circle and its interior (base), a given point not on the plane of the circle (vertex) and all the segments from the point to the circle.A right cone is a cone where the vertex is directly above the centre of the base. If you are talking about a right cone then the radius of the base can be calculated using Pythagorus, a2 + b2 = c2, whereby a = radius, b = height (altitude) and c = slant height.Therefore a2 = c2 - b2 or (radius)2 = (slant height)2 - (altitude)2

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

Slant height is 7.81 inches.

Assuming it is a right cone, use Pythagoras - slant height = hypotenuse, other two sides = radius of base, and height.

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

The slant height is the hypotenuse of the right triangle formed by the height of the cone and the radius of the base. Use the Pythagorean theorem. The Pythagorean theorem (radius)2 + (perp. height)2 = (slant height)2

the slant height of a right circular cone is the distance from any point on the circle to the apex of the cone . The slant height of a cone is given by the formula ,√r2+h2 where r is the radius of the circle and h is the height from the center of the circle to the apex of the cone.

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

A right cone with a radius of 4 and a slant height of 13 has a total surface area of about 213.63 units2

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