The length breadth and height of a room are 8m 50 cm

From the question, it’s given that Length of the room = 8 m 25 cm = 825 cm Breadth of the room = 6 m 75 cm = 675 cm Height of the room = 4 m 50 cm = 450 cm The required longest rod which can measure the room exactly is the HCF of 825, 675 and 450. First, consider 675 and 450 and apply Euclid’s division lemma, 675 = 450 x 1 + 225 450 = 225 x 2 + 0 Therefore, the HCF (675, 450) = 225 Now, consider 225 and the third dimension i.e., 825 By applying Euclid’s division lemma to the above, 825 = 225 x 3 + 150 225 = 150 x 1+75 150 = 75 x 2 + 0 (here the remainder becomes 0) Thus, HCF (225, 825) = 75. Therefore, HCF of 825, 675 and 450 is 75. And, the length of the longest rod is 75 cm or 0.75 m.

NCERT Exemplar Class 8 Maths Chapter 11 Mensuration are part of NCERT Exemplar Class 8 Maths Chapter 11 Mensuration Multiple Choice Questions Question. 1 A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, then how many 1 cubic centimetre cubes will have exactly one of their faces painted? (a) 27 (b) 42 (c) 54 (d) 142 Solution. Question. 2 A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes? (a) 1 : 2 (b) 1 : 3 (c) 1 : 4 (d) 1 : 6 Solution. Question. 3 A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square? (a) 3/4 of original square (b) 1/2 of original square (c) 1/4 of original square (d) 2/3 of original square Solution. (b) Let a be the side of a square sheet. Question.4 What is the area (in sq units) of the largest triangle, that can be fitted into a rectangle of length l units and width w units? (a)lw/2 (b) lw/3 (c) lw/6 (d) lw/4 Solution. Question. 5 If the height of a cylinder becomes1/4 of the original height and the radius is doubled, then which of the following will be true? (a) Volume of the cylinder will be doubled (b) Volume of the cylinder will remain unchanged (c) Volume of the cylinder will be halved (d) Volume of the cylinder will be 1/4 of the original volume Solution. Question. 6 If the height of a cylind...

SOLUTION Given, Length, L = 8 m 50 cm = 850 cm = 2 1 × 5 2 × 17 Breadth, B = 6m 25cm = 625 cm 5 4 Height, H = 4m 75cm = 475 cm = 5 2 × 19 The longest rod that can measure the dimensions of the room exactly, will be equal to the HCF of length,breadth and height of the room. ∴ HCF of L, B and H is 5 2 = 25cm ∴ Length of the longest rod = 25 cm