Question

derive the formula for the curved surface area and total surface area of the frustum of the cone using the symbols as explained.​

Answer 1

Step-by-step explanation:

Frustum of a cone:

Cut a right circular cone with a plane parallel to the base of the cone, then the solid shape between the plane and the base of the cone is called the frustum of a cone.

e.g. Flower pots have a shape as the frustum of a cone.

The surface area and the volume of the frustum of a cone can be calculated using standard formulae.

CSA of the frustum of a cone = πl( r1 + r2).

where r1 = radius of the larger circular face of the frustum, r2 = radius of the smaller circular face of the frustum, and l = slant height of the frustum.

l = h 2 + ( r 1 - r 2 ) 2 and h is the height of the frustum.

TSA of a frustum of a cone = πl(r1 + r2) + πr12 + πr22

Volume of the frustum of a cone = (1/3) πh (r12 + r22 + r1 r2)

frustum of a cone, CSA of the frustum of a cone, TSA of a frustum of a cone, volume of the frustum of a cone,slant height of a frustum of a cone

Answer 2

Frustum of a cone:

Let the radii of the frustum of the cone = R and r

Let the height of the frustum of the cone = h and

The slant height of the frustum of the cone = l

∴ The curved surface area of the frustum of the cone = πl(R + r)

Where, $l^{2} =h^{2} +(R-r)^2$

The total surface area of the frustum of the cone

= Area of base + Area of top + Lateral surface area

= $\pi R^2$ + $\pi r^2$ + πl(R + r)

= π($R^{2} +r^{2}+l(R+r)$ square units

∴ The curved surface area of the frustum of the cone = πl(R + r) square units and

The total surface area of the frustum of the cone = π($R^{2} +r^{2}+l(R+r)$ square units