Chapter 12.3, Problem 33PPS

To determine

Tofind:The surface area of given composite solid, round to the nearest tenth.

Answer to Problem 33PPS

The surface area of the composite solid is $203.0$ inch².

Explanation of Solution

Given information:

The diagram of composite solid is shown in Figure-1.

Formulaused:

The lateral surface area of a cone of radius r and slant height lis given by $L=\pi rl$

Calculations:

The composite figure is made of joining two cones ABD and BDC, each of radius4 inches base to base as shown in Figure-2.

The surface area of composite solid is equal to the sum of lateral areas of two cones.

The height of cone ABD is 6 inches and radius 4 inches. The slant height of cone ABD is

  $l=\sqrt{r^2+h^2}=\sqrt{4^2+6^2}$

  $l=\sqrt{52}$ inches.

The surface area of cone ABD is $S_1=\pi rl=\pi \left(4\right)\left(\sqrt{52}\right)=90.6$ inch².

The height of cone BCD is 8 inches and radius 4 inches. The slant height of cone BCD is

  $l=\sqrt{r^2+h^2}=\sqrt{4^2+8^2}$

  $l=\sqrt{80}$ inches.

The surface area of cone BCD is $S_2=\pi rl=\pi \left(4\right)\left(\sqrt{80}\right)=112.4$ inch².

Therefore, the surface area of the composite solid is $S=90.6+112.4=203.0$ inch².

Conclusion:

The surface area of the composite solid is $203.0$ inch².