Question

If the radii of the circular ends of a frustum
shaped object which is 30 cm high are 14 cm
and 7 cm. Find the total surface area and
capacity of the object.

Answer 1

Answer:

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Answer 2

Total surface area of object =2802.8 square cm

Capacity of object=10780 cubic cm

Step-by-step explanation:

Let $r_1=14 cm$

$r_2=7 cm$

Height of object=h=30 cm

Slant height of frustum=$l=\sqrt{r_1-r_2)^2+h^2}$

Slant height of frustum=$l=\sqrt{(14-7)^2+(30)^2}=30.8 cm$

Total surface area of frustum=$\pi(r_1+r_2)l+\pi r^2_1+\pi r^2_2$

$\pi=\frac{22}{7}$

Using the formula

Total surface area of object =$\frac{22}{7}(14+7)(30.8)+\frac{22}{7}(14)^2+\frac{22}{7}(7)^2$

Total surface area of object =2802.8 square cm

Volume of frustum=$\frac{1}{3}\pi h(r^2_1+r^2_2+r_1r_2)$

Volume of frustum=$\frac{1}{3}\times \frac{22}{7}\times 30((14)^2+7^2+14\times 7)$

Capacity of object=Volume of frustum=10780 cubic cm

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