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একটি আয়তাকার কাগজের টুকরো 44 সেমি লম্বা এবং 89 সেমি চওড়া। কাগজটিকে তার দৈর্ঘ্য বরাবর মুড়িয়ে একটি চোঙ তৈরি করা হয়। চোঙটির বক্রতলের ক্ষেত্রফল নির্ণয় করুন।
3961 সেমি²
3931 সেমি²
3902 সেমি²
3916 সেমি²
3961 সেমি2
When a rectangle is rolled along one side, the other side becomes the circumference (2πr) and the side being rolled becomes the height (h). Thus, CSA=Width×Length=89×44.
Length of paper L = 89 cm, Width of paper W = 44 cm. Cylinder is formed by rolling along the length.
CSA=2πrh
When a rectangle is rolled along one side, the other side becomes the circumference (2πr) and the side being rolled becomes the height (h). Thus, CSA=Width×Length=89×44.
Many students try to calculate the radius and height separately, but the curved surface area of a rolled cylinder is simply the area of the original rectangle.
Identify dimensions
The rectangular paper has dimensions 89 cm and 44 cm. Rolling it along its length makes the height equal to the length and the circumference equal to the width.
h=89 cm,C=44 cm
Relate area to rectangle
The Curved Surface Area (CSA) of a cylinder formed from a sheet of paper is equivalent to the surface area of the rectangle itself.
CSA=Length×Width
Calculate
Multiply the given dimensions to find the total area.
CSA=89×44=3916 cm2
D is correct because the area of the rectangle is 89 * 44 = 3916 cm².
This concept of 'unfolding' surfaces is crucial for problems involving lateral surface areas of cones and cylinders in 3D geometry.