Question

total surface area of a cone is 616 sq. cm.If the slant height of the cone is three times the radius of its base.Find its slant height.

Answer 1

hiii!!!

here's ur answer...

length = slant height

ATQ,

the slant height of the cone is three times the radius of it's base.

let the radius be x.

therefore slant height is 3x.

TSA ( total surface area ) of the cone = 616cm²

therefore πrl + πr² = 616cm²

==> 22/7 × x × 3x + 22/7 × x × x = 616cm²

==> 22/7 × 3x² + 22/7 × x² = 616cm²

==> 66x²/7 + 22x²/7 = 616cm²

==> 88x²/7 = 616cm²

==> 88x² = 616/7

==> 88x² = 88

==> x² = 88/88

==> x² = 1

==> x = √1

==> x = 1cm

hence, radius of the cone is 1cm and slant height is = 3x = 3 × 1 = 3cm

hope it's right...

:D