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Q.2 / 40:A cuboid of dimension 51,85 and 102 cm is first
painted by green colour then it is cut into minimum
possible identical cubes. Now the total surface area of all
those faces of cubes which are not green is:
एक घनाभ जिसकी माप 51,85 और 102 cm है को पहले हरे रंह से रंगा
जाता फिर निम्नतम संभावित छोटे से छोटे घनाभों में काटा जाता है। अब
उन सभी सतहों का क्षेत्रफल जो क्या होगा जो हरे रंग से नहीं रंगी हैं?​

Answer 1

Given :- :A cuboid of dimension 51,85 and 102 cm is first painted by green colour then it is cut into minimum possible identical cubes. Now the total surface area of all those faces of cubes which are not green is ?

Answer :-

Dimensions of cuboid are :-

→ 51 = 17 * 3

→ 85 = 17 * 5

→ 102 = 17 * 6

so,

→ Minimum possible identical cubes cut from cuboid is = 3 * 5 * 6 = 90 cubes .

and,

→ side of cubes so formed is = 17 cm .

now,

→ TSA of all those faces of cubes which are not green will be = TSA of 90 cubes - TSA of cuboid .

we know that,

• TSA of cube = 6 * (side)²
• TSA of cuboid = 2(LB + BH + HL)

then,

→ Required TSA = 90 * (6 * 17²) - 2(51 * 85 + 85 * 102 + 102 * 51)

→ Required TSA = 90 * 1734 - 2(4335 + 8670 + 5202)

→ Required TSA = 156060 - 2 * 18207

→ Required TSA = 156060 - 36414

→ Required TSA = 119646 cm² (Ans.)

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