Question 4 - Figure it out - Page 150-152 - Chapter 7 Class 8 - Area (Ganita Prakash II)

Transcript

Question 4 Find the area of the spiral tube shown in the figure. The tube has the same width throughout. [Hint: There are different ways of finding the area. Here is one method.] What should be the length of the straight tube if it is to have the same area as the bent tube on the left? Let’s look at our hint. It tells us if we straighten our tube Thus, if we straighten our tube The area at the turn gets counted twice, so we remove it once And, Area of turn = Area of Square of side 1 = 1 × 1 = 1 square unit Finding Area of Spiral Now, Sum of all outer numbers given = 20 + 20 + 20 + 15 + 15 + 10 + 10 + 5 + 5 = 120 units Thus, if we straighten the spiral, we get a rectangle of side 120 × 1 Thus, Area of rectangle of side 120 × 1 = 120 × 1 = 120 square units Count the 90-degree corners There are 8 corners where the pipes overlap by a 1 × 1 square. So, these area will be removed ∴ Area to removed = 1 × 8 = 8 square units Thus, Total Area = 120 – 8 = 112 square units = 8 square units Thus, Total Area = 120 – 8 = 112 square units Note: Our overlapping figure looks like