Three cubes of sides 6 cm, 8 cm and 1 cm are melted to form a new cube

1.	Three cubes of sides 6 cm, 8 cm and 1 cm are melted to form a new cube. The surface area of the new cube is:‐ 1. 486 sq cm2. 496 sq cm3. 586 sq cm4. 658 sq cm
Answer» Correct Answer - Option 1 : 486 sq cm Surface area of cube = 6 × a², where a is side of the cube Volume of cube = a³ Volume of cube with side 1 cm = 1³ = 1 cm³ Volume of cube with side 6 cm = 6³ = 216 cm³ Volume of cube with side 8 cm = 8³ = 512 cm³ Total Volume = 1 + 216 + 512 = 729 cm³ Side of new cube = a cm Volume of new cube = a³ cm³ a³ = 729 ⇒ a = 9 Side of cube = 9 cm Surface Area = 6 × a² = 6 × 9² = 486 cm² ∴ Surface area of the new formed cube 486 cm²

Three cubes of sides 6 cm, 8 cm and 1 cm are melted to form a new cube. The surface area of the new cube is:‐ 1. 486 sq cm2. 496 sq cm3. 586 sq cm4. 658 sq cm

Answer» Correct Answer - Option 1 : 486 sq cm

Surface area of cube = 6 × a², where a is side of the cube

Volume of cube = a³

Volume of cube with side 1 cm = 1³ = 1 cm³

Volume of cube with side 6 cm = 6³ = 216 cm³

Volume of cube with side 8 cm = 8³ = 512 cm³

Total Volume = 1 + 216 + 512 = 729 cm³

Side of new cube = a cm

Volume of new cube = a³ cm³

a³ = 729

⇒ a = 9

Side of cube = 9 cm

Surface Area = 6 × a² = 6 × 9² = 486 cm²

∴ Surface area of the new formed cube 486 cm²

Discussion

No Comment Found

Related InterviewSolutions

The dimensions of a rectangle are 24 cm and 16 cm. If the circumference of the circle is 110% of the perimeter of rectangle, then what will be the area of the circle?1. 550 cm22. 792 cm23. 616 cm24. 921 cm25. 587 cm2
Forty-two cubes each of side 1 cm are glued together to form a solid cuboid. If the perimeter of the base of the cuboid is 18cm, then its height, in cm, is1. 12. 23. 34. 4
If the area of a right-angled isosceles triangle is 676 cm2, then the length of its hypotenuse is:1. 53 cm2. 52 cm3. 50 cm4. 51 cm
The number of solid spheres ,each of diameter 3 cm that could be moulded to form a solid metal cylinder of height 54 cm and diameter 4 cm is?1. 162. 243. 364. 48
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the radius of each such ball is ___________.1. 1.25 cm2. 2.5 cm3. 3.75 cm4. 5 cm
The ratio of the length and the breadth of a rectangular plot is 6 : 5 respectively, if the breadth of the plot is 34 meters less than the length, what is the perimeter of the rectangular plot?1. 408 meters2. 814 meters3. 374 meters4. 748 meters
A rectangular swimming pool of length 30 m, breadth 25 m and 4.5 m depth is to be constructed with tiles of square shape. Find how many such tiles needed (approx) to cover the swimming pool. It is given that the side of the tiles is 40 cm1. 75642. 77653. 78624. 7781
The perimeter of the rectangle of breadth 16cm is 98cm. The area of a rectangle and curved surface area of a cylinder is the same. The difference between the height and radius of the cylinder is 5cm. Find the volume of a cylinder.1. 1848 cubic.cm2. 1526 cubic.cm3. 1330 cubic.cm4. 1240 cubic.cm5. 1642 cubic.cm
Find the length of the longest rod that can be placed in a hall of 10 m length, 6 m breadth and 4 m height.1. 2√19 m2. 2√ 38m3. 4√38 m4. 3√38 m
The side of an equilateral triangle is 15cm. The equal side of isosceles triangle is 14cm. The perimeter of isosceles triangle and equilateral triangle is same. Find the ratio of sides of an isosceles triangle.1. 18 : 15 : 152. 17 : 15 : 153. 14 : 14 : 174. 14 : 14 : 195. 17 : 17 : 14

Three cubes of sides 6 cm, 8 cm and 1 cm are melted to form a new cube. The surface area of the new cube is:‐ 1. 486 sq cm2. 496 sq cm3. 586 sq cm4. 658 sq cm

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment