Question

In Fig. 16.74, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (use π=22/7 and √5=2.236)

Answer 1

TSA of the frustum = 350.59 sq.cm.

Step-by-step explanation:

From the figure, we find that the figure is a frustum.

Height of the frustum = 12 - 4 = 8cm

Bottom radius R = 6 cm

Top radius R = 2 cm

Slant height of frustum l = root of (h² + (R-r)²) = root (8² + (6-2)²)

   = 4√5 cm

Curved Surface area of frustum = π(R+r)l = 22/7 * 8 * 4√5 = 224.88 sq.cm.

Area of base = πr² = 22/7 * 6 * 6 = 113.14 sq.cm.

Area of top = πR² =  22/7 * 2 * 2 = 12.57 sq.cm.

Total surface area of the frustum = 224.88 + 113.14 + 12.57 = 350.59 sq.cm.