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The dimensions of a metallic cuboid are 100 cm × 80 cm × 64 cm. It is melted and recast into a cube. Answer the following questions that follow: (a) If the edge of the cube be ‘a’, then volume of cube is given by: (i) a2(ii) a3 (iii) a (iv) None. (b) Formula for finding value of cuboid is: (i) l × b × ℎ(ii) \(\frac{l \times b}{h}\)(iii) \(\frac{b \times h}{l^2}\)(iv) None. (c) In our context, volume of cuboid is: (i) 512000 cm3 (ii) 104200 cm3 (iii) 9234 cm.3 (iv) None. (d) Volume of the cube is: (i) 512000 cm3 (ii) 104200 cm3 (iii) 9234 cm3 (iv) None. (e) Surface area of the cube is: (i) 5120 cm2 (ii) 104200 cm2 (iii) 38400 cm2 (iv) None. |
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Answer» The dimensions of the cuboid are 100 cm × 80 cm × 64 cm. Therefore, the volume of the cuboid is V = l × b × h = 100 × 80 × 64 = 512000 cm3 . Given that the cuboid is melted and recast into a cube. ∴ The volume of the cube = the volume of the cuboid. ∴ The volume of the cube = 512000 cm3 . (a) If the edge of the cube is a then, the volume of the cube is given by = a3 . Hence, option (ii) is correct. (b) Formula of finding volume of cuboid = l × b × ℎ. Hence, option (i) is correct. (c) Volume of cuboid is V = l ×b × ℎ. = 100 × 80 × 64 = 512000 cm3 . Hence, option (i) is correct. (d) Volume of the cube = 512000 cm3 . Hence, option (i) is correct. (e) Since, volume of the cube whose side length is a is given by a3 . And volume of the cube is 512000 cm3 . ∴ a3 = 512000 = 83×103 = 803 ⇒ a = 80 cm. Hence, the side length of the cube is a = 80 cm. ∴ Surface area of the cube = 6a2 = 6×802 = 38400 cm2 . Hence, option (iii) is correct. (a) (i) a3 (b) (i) l × b × h (c) (i) 512000 cm3 (d) (i) 512000 cm3 (e) (iii) 38400 cm2 |
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