Question

the diagram shows an engine component which consists of a rectangular shape with holes drilled in it. the area of the remaining material, correct to the nearest cm² is equal to:

Explanation:

Step1: Calculate area of rectangle

The formula for the area of a rectangle is \( A_{rectangle} = length \times width \). Here, length is 50 cm and width is 19 cm.
\( A_{rectangle} = 50 \times 19 = 950 \, cm^2 \)

Step2: Calculate area of one circle

The formula for the area of a circle is \( A_{circle} = \pi r^2 \), where radius \( r = \frac{diameter}{2} \). The diameter of each circle is 7 cm, so \( r = \frac{7}{2} = 3.5 \, cm \).
\( A_{circle} = \pi \times (3.5)^2 = \pi \times 12.25 \approx 38.4845 \, cm^2 \)

Step3: Calculate total area of four circles

There are 4 circles, so total area of circles is \( 4 \times A_{circle} \).
\( 4 \times 38.4845 \approx 153.938 \, cm^2 \)

Step4: Calculate remaining area

Remaining area = Area of rectangle - Total area of circles.
\( 950 - 153.938 \approx 796.062 \, cm^2 \), which rounds to 796 \( cm^2 \) (correct to nearest \( cm^2 \))

Answer:

796