Question

The curved surface area of a cone is 180π cm², and its base area is 144π cm². Find its total surface area and volume.​

Answer 1

since base area is 144πcm sq by using the formula area of circle is equal to πr square

144π = πr square

( π get's cancelled)

144 = r square

r = √144 = 12

CSA of cone = πrl

180 = πrl

180 = 22/7 × 12 × l

l = 180 × 7 / 22 × 12

l = 105/11

l= 9.54 cm

TSA of Cone = πrl + πr square

= πr(l + r)

= 22/7(9.54+12)

=22/7 × 21.54

= 22× 3.07 (approx) cm sq

= 67.54 cm sq

h = √l sq + r sq

h = √(9.54)sq + 12 sq

h = √91.011+ 144

h = √235.011

h = 15.33 cm ( approx)

volume of cone = πr sq h

= 22/7 × 144 × 15.33

= 6937.92 cm cube.