Question

the perimeter of the circular base of a cone is 132 cm and its vertical height is 28 cm find the curved surface area total surface area and volume of the cone​

Answer 1

Answer:

i. Curved surface area = 2310 $cm^{2}$

ii. Total surface area = 3696 $cm^{2}$

iii. volume = 12936 $cm^{3}$

Step-by-step explanation:

Perimeter of the circular base = circumference of the circle = 132 cm

circumference of a circle = 2$\pi$r

132 = 2$\pi$r

r = $\frac{132}{2\pi }$

 = $\frac{66}{\pi }$

r = 66 x $\frac{7}{22}$

 = 3 x 7

 = 21

radius = 21 cm

vertical height, h = 28 cm

Thus applying the Pythagoras theorem,

$l^{2}$ = $h^{2}$ + $r^{2}$

  = $28^{2}$ + $21^{2}$

  = 784 + 441

  = 1225

l = $\sqrt{1225}$

l = 35 cm

The slant height is 35 cm.

i. Curved surface area = $\pi$rl

                           = $\frac{22}{7}$ x 21 x 35

                           = 22 x 3 x 35

                           = 2310

curved surface area of the cone is 2310 $cm^{2}$.

ii. Total surface area = $\pi r^{2}$ + $\pi$rl

                                  = $\pi$r(r + l)

                                  = $\frac{22}{7}$ x 21 (21 + 35)

                                  = 22 x 3 x 56

                                  = 3696

The total surface area of the cone is 3696 $cm^{2}$.

iii. volume of a cone = $\frac{1}{3}$$\pi r^{2}$h

                                  =  $\frac{1}{3}$ x $\frac{22}{7}$ x $21^{2}$ x 28

                                   = 12936

The volume of the cone is 12936 $cm^{3}$