Question

A sector of central angle 30dgeree is cut out from a circle of radius 12 centimetres and is rolled a up into a cone. a) What is its slant height ? b) What is its radius ? c) What is its curved surface area

Answer 1

Answer:

a) 12cm

b) 11 cm

c) 414.85 $cm^2$

Step-by-step explanation:

a) Slant height of cone = radius of the circle from which the cone is made

= 12cm

b) Let the radius of the cone be R cm

Curved surface area of the cone = remaining area of the circle

remaining area or the  area of the major sector of the circle = $\pi r^r- \frac{30}{360} (\pi r^2)\\r=12\\\pi r^2[1-\frac{1}{12}]\\\frac{11\pi r^2}{12}\\=> 132\pi$

Curved surface area = $132\pi$

curved surface are of a cone = $\pi rl$

$\pi R(12) = 132\pi \\=> R= 11 cm$

c) CSA= 132× $\frac{22}{7}$

          => 414.85$cm^2$