Chapter 12.5, Problem 26PPS

To determine

To determine the volume of the cone.

Answer to Problem 26PPS

  $471.3{\text{ inch}}^3$

Explanation of Solution

Given:

  

Formula used:

Volume of the cone $V=\frac{1}{3}\pi r^{2}h$

  $\left[r=\text{radius, }h\text{=}\text{height}\right]$

Calculation:

The given figure,

  

Splitting the image in two parts,

  

Taking part I:

  

Height of the cone $=7$ inch

Radius of the cone $=5$ inch

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\pi r^{2}h$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(5)}^2\times 7$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times 25\times 7$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 549.778$

  $\Rightarrow$ Volume of the cone $V=183.259$

Rounding off to nearest tenth,

  $V=183.3 {\text{inch}}^3$

Taking part II:

  

Height of the cone $=11$ inch

Radius of the cone $=5$ inch

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\pi r^{2}h$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(5)}^2\times 11$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times 25\times 11$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 863.937$

  $\Rightarrow$ Volume of the cone $V=287.979$

Rounding off to tenth,

  $\Rightarrow$ Volume of the cone $V\approx 288{\text{ inch}}^3$

Total volume is sum of volume of part I and part II

  $\Rightarrow \text{Total Volume}=183.3 {\text{inch}}^3+288{\text{ inch}}^3$

  $\Rightarrow \text{Total Volume}=471.3{\text{ inch}}^3$

Conclusion:

Therefore, the volume of the cone is $471.3{\text{ inch}}^3$ .