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### Mathematical Skills | Mensuration

 Q. No. 1: A piece of string is 50cm long. It is cut into three pieces such that the longest piece is three times as long as the shortest piece and the third piece is 20cm shorter than the longest piece. If the pieces are joined to form a triangular region, find the area (in sq. cm) of the region formed. A : 100 B : 120 C : 160 D : Data inconsistent Solution
 Q. No. 2: Sachin had a triangle in his mind, its longest side has a length of 10 and one of its sides has a length of 5.What is the exact length of its third side, if the area of the triangle is 20? A : √65 B : √60 C : √175 D : √72 Solution
 Q. No. 3: A thin rectangular strip of cloth which is 80cm long is cut into 3 pieces along its length. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 46cm shorter than the longest piece. Find the length of the shortest piece. A : 54cm B : 10cm C : 8cm D : 18cm Solution
 Q. No. 4: A rectangular sheet of paper was folded along the line joining the mid points of its longer sides. The rectangle which resulted had the same ratio of its longer and the shorter sides as that of the original rectangle. If the breadth of the original rectangle is √2 cm, find the area (in sq cm) of the smaller rectangle. A : 3√2/2 B : 3√2/4 C : √2 D : 2√2 Solution
 Q. No. 5: A cuboid has a volume of 64 cubic units. Find the minimum possible vale (in units) of the sum of the lengths of the edges of the cuboid. A : 36 B : 40 C : 42 D : 48 Solution
 Q. No. 6: A small cylinder container is of height 7cm. the outer radius of the container is 8cm and inner radius is 6cm. Water whose density is 1gm/cm3 is filled to the brim in the container. If the density of the material of the container is 16gm/cm3, find the weight of the container filled completely with water.(The weight of the bottom is negligible). A : 13376 gm B : 7920 gm C : 14168 gm D : 10648 gm Solution
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