Question

The perimeters of the ends of the frustum of a cone are 207.24 cm and 169.56 cm. If the height of the frustum be 8 cm, find the whole surface area of the frustum. (Use = 3.14)

Answer 1

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Answer 2

Answer:

$7592.52 cm^2$

Step-by-step explanation:

Circumference of one end of frustum = $2 \pi r$

So, $2 \pi r=207.24$

$2 \times 3.14 \times r=207.24$

$r=\frac{207.24}{2 \times 3.14}$

$r=33$

So, the radius of one end is 33 cm

Circumference of other end of frustum = $2 \pi r$

So, $2 \pi r=169.56$

$2 \times 3.14 \times r=169.56$

$r=\frac{169.56}{2 \times 3.14}$

$r=27$

So, the radius of other end is 33 cm

Height of frustum = 8 cm

Total surface area of frustum = $\pi (r+R)\sqrt{(R-r)^2+h^2}+\pi r^2 +\pi R^2$

                                                = $3.14 \times (27+33)\sqrt{(33-27)^2+8^2}+3.14 \times 27^2 +3.14 \times  33^2$

                                                = $7592.52 cm^2$

Hence  the whole surface area of the frustum is  $7592.52 cm^2$