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CBSE Class 8 Mathematics Question 4 of 9

Area — Question 4

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4
Question
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?
Answer

After naming the figure, The area of the spiral tube = Area of the rectangle, ABEC + Area of the rectangle, DEGF + Area of the rectangle, GHIJ + Area of the rectangle, JKML + Area of the rectangle, NOPL + Area of the rectangle, PQRS + Area of the rectangle, STUV + Area of the rectangle, VWYX + Area of the rectangle, XZA 1 B 1 = AC × AB + EG × DE + IH × JI + LJ × LM + NO × NL + PQ × PS + UT × ST + VX × VW + ZA 1 × A 1 B 1 = 20 × 1 + 18 × 1 + 20 × 1 + 13 × 1 + 15 × 1 + 8 × 1 + 10 × 1 + 3 × 1 + 5 × 1 = 20 + 18 + 20 + 13 + 15 + 8 + 10 + 3 + 5 = 112 sq. units Thus, the area of the spiral tube is 112 sq. units. Let the length of the straight tube be x. The area of the bent tube on the left = Area of rectangle, BACD + Area of rectangle, BGFE = AC × CD + BG × BE = 5 × 1 + 4 × 1 = 9 sq. units Area of straight tube = x × 1 Area of bent tube = 9 sq. units According to the question, both are the same. So x × 1 = 9 ⇒ x = 9 units.