The height of a solid cone is 12 cm and the area of the circular base

1.	The height of a solid cone is 12 cm and the area of the circular base is 64π cm2. A plane parallel to the base of the cone cuts through the cone 9 cm above the vertex of the cone, the area of the base of the new cone so formed is :A. 9π cm2 B. 16π cm2 C. 25π cm2 D. 36π cm2
Answer» Option : (D) We have, Height of cone = 12cm Area of circular base = 64π cm² Height from the vertex of small cone = 9 cm πr² = 64π r²= 64 Radius of base = 8cm From similarity triangle = \(\frac{12}{8}\) = \(\frac{9}{R}\) = R = \(\frac{9\times8}{12}\) = 6 cm R = radius of small cone Area of small cone = πr² = π(6)² = 36π cm²

The height of a solid cone is 12 cm and the area of the circular base is 64π cm2. A plane parallel to the base of the cone cuts through the cone 9 cm above the vertex of the cone, the area of the base of the new cone so formed is :A. 9π cm2 B. 16π cm2 C. 25π cm2 D. 36π cm2

Answer»

Option : (D)

We have,

Height of cone = 12cm

Area of circular base = 64π cm²

Height from the vertex of small cone = 9 cm

πr² = 64π

r²= 64

Radius of base = 8cm

From similarity triangle = \(\frac{12}{8}\) = \(\frac{9}{R}\)

= R = \(\frac{9\times8}{12}\)

= 6 cm

R = radius of small cone

Area of small cone = πr²

= π(6)²

= 36π cm²