Chapter 12, Problem 8MCQ

To determine

To determine lateral area and surface area.

Answer to Problem 8MCQ

  $\approx 2591.8{\text{ yard}}^2$ and $\approx 3779.7{\text{ yard}}^2$

Explanation of Solution

Given:

  

Formula used:

Lateral area of a cylinder $A=2\pi rh$

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

Surface area of a cylinder $A=2\pi rh+2\pi r^2$

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

Calculation:

  

Diameter of the cylinder $=27.5$ yard

Radius of the cylinder $=\frac{27.5}{2}=13.75$ yard

Height of the cylinder $=30$ yard

Now, lateral area of a cylinder $A=2\pi rh$

Lateral area of a cylinder $=2\pi \times 13.75\times 30$

  $=2\pi \times 412.5$

  $=2591.813$

  $\approx 2591.8{\text{ yard}}^2$

And surface area of a cylinder $A=2\pi rh+2\pi r^2$

Surface area of a cylinder $=2\pi \times 13.75\times 30+2\pi \times {(13.75)}^2$

  $=2591.813+1187.914$

  $=3779.727$

  $\approx 3779.7{\text{ yard}}^2$

Conclusion:

Therefore, lateral area and surface area of the given figure are $\approx 2591.8{\text{ yard}}^2$ and $\approx 3779.7{\text{ yard}}^2$ respectively.