An irregularly shaped portion, as shown in the picture below, was cut from a rectangular iron sheet which has an area of 19,125 m² - NSC Technical Mathematics - Question 11 - 2019 - Paper 2

First, we calculate two thirds of the area of the iron sheet:

$\text{Area of iron sheet} = 19125 m^2 \\ \text{Area of irregular portion} = \frac{2}{3} \times 19125 = 12750 m^2$

Knowing the lengths of the six ordinates, we apply them to find the equivalent area. Let the six ordinates be calculated:

$A = \frac{1.8 + b + 1.4 + 1.3 + 1.8 + q}{2} \times 7.5$

Given the area is 12750 m², we solve for q. Simplifying:

$(1.8 + 1.4 + 1.3 + 1.8 + q) imes 3.75 = 12750$

Solving yields:

$q = 2.2 m$

To calculate the height of the rectangular prism, we can use the volume formula for the rectangular section:

$V = l \times b \times h \\ 70 = 3.5 \times 10 \times h$

Rearranging gives us:

$h = \frac{70}{3.5 \times 10} = 2 m$

The length of the radius (r) of the half cylinder can be derived from the given dimensions. It is equal to the breadth of the rectangular prism:

$r = \frac{3.5}{2} = 1.75 m$

To find the total surface area (SA), we sum the surface areas of the rectangular prism and the half cylinder:

First, calculate the surface area of the rectangular prism:

$SA_{prism} = 2 \times (b \times h) + 2 \times (l \times h)$ $SA_{prism} = 2 \times (3.5 \times 2) + 2 \times (10 \times 2) = 54 m²$

Next, for the half cylinder:

$SA_{cylinder} = \frac{1}{2} \times (2\pi r^2 + 2\pi rh)$ Substituting the values:

$= \frac{1}{2} \times \left( 2\pi (1.75)^2 + 2\pi (1.75)(10) \right)$ $= 20.56 m²$

So,

$SA_{total} = 54 + 20.56 = 118.56 m²$

Thus, yes, the total surface area is indeed less than 120 m².