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Notes On Cubes And Cuboids

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Published in: Mathematics
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This is a practice material for "Cubes & Cuboids". The solutions can be given on demand.

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  1. 1. 2. 3. 4. 5. 6. 7. 8. 9. Work Sheet — Cubes and Cuboids By Kolli Naveen Kumar The lateral surface area of a cuboid whose length, breadth and height are 2cm, lcm and lcm respectively, is equal to the total surface area of a cube. Find the length of each edge of the cube. A cake is in the shape of a cuboid with two of its edges measuring 10cm and 4cm. Find the length of the third edge if it weighs 450gms, given that each cubic cm of the cake weighs 1.5gm. A tunnel whose length, width and depth are 150m, 1.5m and 1m respectively is dug and the mud so obtained is used to build a wall whose width and height are 20cm and 150cm respectively. Find the wall's length. An ice cube measuring lcm x lcm x lcm melts to half its volume in 2min, but takes the shape of a cuboid with length and breadth 0.8cm and 0.6cm respectively. Find its new thickness after 2min. The length and breadth of a book are 12cm and 7.5cm respectively. Assuming that the cover pages are of the same thickness as each of the other pages, find the thickness of each page (in mm), given that the volume of the book is 45cu.cm and there are 100 pages in the book including the cover pages. 720 cubical bricks are used to construct a wall whose dimensions are 450cm x 360cm x 15cm. Find the length of each edge of a brick. A square cardboard sheet with dimensions 2m x 2m is used to make a closed cubical box whose volume is 0.512cu.m. Find the wastage (in sq.cm) while making the box. A cuboid is cut on its length into three equal cubes each of its edges measuring 2cm. Find the total surface area of the cuboid. The surface area and thickness of a rectangular wooden cardboard are 5000sq.cm and 1.5cm respectively. If the weight of lcu.cm of wood is 20gm, find the total weight of the cardboard. 10. The ratio of the length, breadth and height of a cuboid is 5:2:1. If its surface area is 850sq.cm, find its volume. 11. If the edge of a cube is increased by 5%, what is the percentage increase in its: a. Surface area b. Volume 12. If the length and breadth of a cuboid are increased by 2% and 3% respectively, what should be the percentage decrease in its height in order to keep its volume same? 13. The ratio of the surface areas of two cubes is 1:4. Find the ratio of their volumes. 14. If the length, breadth and height of a cuboid are increased by 1%, 2% and 3% respectively, then its volume is increased by 15. A cubical vessel whose edge is 5cm containing water to its brim is poured into a cuboidal container with length and breadth 8cm and 6cm respectively. Find the level of water in the cuboidal container.

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