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Q: What is the slant height ℓ of a cone that has a Lateral Surface Area of 285 sq. cm. and a radius of 10 cm?

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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.

The slant height cannot be larger than the base radius.

Why do you need to FIND the slant height if you have the [lateral height and] slant height?

The lateral surface area is A = pi*(radius)*(slant height), where (slant height) = sqrt(r^2 + h^2). So A = pi*(5 in)*sqrt((5 in)2+(19 in)2) = 308.6125 square inches

The lateral area is, I think, 35pi and the surface area is 60pi.188.40 units sq.

Related questions

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

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.

3

The slant height cannot be larger than the base radius.

The lateral surface area is 18.85 square inches.

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.

Why do you need to FIND the slant height if you have the [lateral height and] slant height?

The lateral surface area is A = pi*(radius)*(slant height), where (slant height) = sqrt(r^2 + h^2). So A = pi*(5 in)*sqrt((5 in)2+(19 in)2) = 308.6125 square inches

The lateral area is, I think, 35pi and the surface area is 60pi.188.40 units sq.

Knowing the slant height helps because it represents the height of the triangle that makes up each lateral face. So, the slant height helps you to find the surface area of each lateral face.

11 units.

37.7 units2