When length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm3. Find its side. How much will its volume decrease, if length of each side of it is reduced by 20% ?

Let `a` be the side of the original cube. Side of the new cube = a \+ 3 Volume of the new cube = a3 \+ 2457 ⇒ a3 \+ 2457 = (a \+ 3)3 ⇒ a3 \+ 2457 = a3 \+ 33 \+ 3 x a2 x 3 \+ 3 x a x 32 ⇒ \+ 2457 = \+ 27 \+ 9a2 \+ 27a ⇒ 2457 = 27 \+ 9a2 \+ 27a ⇒ 9a2 \+ 27a \- 2457 \+ 27 = 0 ⇒ 9a2 \+ 27a \- 2430 = 0 ⇒ a2 \+ 3a \- 270 = 0 ⇒ a2 \+ 18a \- 15a \- 270 = 0 ⇒ a(a \+ 18) \- 15(a \+ 18) = 0 ⇒ (a \+ 18)(a \- 15) = 0 ⇒ a = \-18 or 15 Since the side cannot be negative, the side of the original cube, a = 15 cm. Volume of original cube = side3 = (15)3 cm3 = 3375 cm3 When the length of side is reduced by 20%. New side of the cube = side \- 20% of side = 15 \- x 15 = 15 \- x 15 = 15 \- 3 = 12 cm New volume of the cube = side3 = (12)3 cm3 = 1728 cm3 Decrease in volume = 3375 \- 1728 cm3 = 1647 cm3 Hence, the side of the original cube is 15 cm and the decrease in volume is 1647 cm3.

Mathematics

When length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm³. Find its side. How much will its volume decrease, if length of each side of it is reduced by 20% ?

Mensuration

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Mathematics

When length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm³. Find its side. How much will its volume decrease, if length of each side of it is reduced by 20% ?

Mensuration

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Mathematics

When length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm3. Find its side. How much will its volume decrease, if length of each side of it is reduced by 20% ?

Mensuration

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