Bissoy.com
Doctors Medicines MCQs Q&A

A metal cube of edge 18 cm is melted to form three smaller cubes, which are unequal in dimensions. If the edges of two smaller cubes are 9 cm and 15 cm, what is the surface area in (cm2) of the third smaller cube? 

A metal cube of edge 18 cm is melted to form three smaller cubes, which are unequal in dimensions. If the edges of two smaller cubes are 9 cm and 15 cm, what is the surface area in (cm2) of the third smaller cube?  Correct Answer 864

Given:

Edge of a metal cube = 18 cm

The edge of the two smaller cubes = 9 cm and 15 cm

Formula used:

Volume of cube = a3

Surface area of cube = 6a2

Calculation:

According to the question

Volume of a metal cube = Volume of three smaller cube

⇒ (18)3 = (9)3 + (15)3 + C3

⇒ 5832 = 729 + 3375 + C3

⇒ 5832 = 4104 + C3

⇒ C3 = (5832 – 4104)

⇒ C3 = 1728

⇒ C = 12 cm

Now,

The surface area of cube = (6 × 12 × 12) cm2

⇒ 864 cm2

∴ The surface area of the third smaller cube is 864 cm2

Related Questions

Some small cubes of same height 7 cm but variable length and width are put inside a large cuboid of height 21 cm. Length and width of cuboid is 32 cm and 24 cm, respectively. Small cubes are put such that cubes at the bottom most layer is of similar base area; second layer contains all the cubes of similar base area and third layer have all the cubes of similar base area. Which of the following statement(s) given below is / are TRUE? A: If side of each small cubes at bottom most layer is 8 cm, then maximum number of small cubes that can be put at bottom most layer is 12. B: If maximum of 48 cubes can be put at second layer, then side of each cube at second layer is 6 cm. C: If side of each small cubes at third layer is 1.6 cm, then maximum number of small cubes that can be put at third layer is 300.
The accompanying image shows a large cube made of dark and white small sugar cubes. Small cubes of the diagonally arranged row of the bottom surface of the large cube, small cubes of the row with one face on the right-hand surface of the large cube, small cubes of the row with one face on the front surface of the large cube, and small cubes of the column with one face on the top of large cube surface are all dark. Select the number of small white cubes of the large cube.
A metal solid cube of edge 24 cm is melted and made into three small cubes. If the edges of two small cubes are 12 cm and 16 cm, then what is the surface area of the third small cube?
The ratio of the length of diagonal of two cubes is 2 ∶ 3 and the difference between the total surface area of the bigger cube and the lateral surface area of the smaller cube is 342 cm2. Find the total surface area of a statue which is formed by placing the smaller cube upon the bigger cube.
The areas of three adjacent faces of a cuboidal solid block of wax are 216 cm2, 96 cm2 and 144 cm2. It is melted and 8 cubes of the same size are formed from it. What is the lateral surface area (in cm2) of 3 such cubes?
Three solid metal cubes of edges 4 cm, 6 cm, and 7 cm are melted to form a new cube. But 111 cm3 volume of the metal is lost in the process. What is the total surface area of the new cube?
Which of the following statement(s) given below is / are TRUE? A: A large solid cube is melted and casted into 3375 small cubes of side 1.6 cm, then side of large cube is 24 cm. B: Total surface area of a hemisphere of total volume 2425.5 cm3 is 693 cm2. C: Height of a cylinder of radius 14 cm and total surface area 2288 cm is 12 cm2. 
A cube of volume 64 cm3 is is cut into two smaller and identical cuboids. The faces of dimensions 4 × 4 of one of the cuboids are painted with black color and the rest of its faces are painted with yellow color. One pair of adjacent faces that do not include any face of dimensions 4 × 4 of the other cuboid are painted with yellow color and the rest of its faces are painted with black color. Now each of two cuboids are cut into 32 smaller and identical cubes. How many of the smaller cubes have exactly three colored faces?
Three solid iron cubes of edges 6 cm, 7 cm, and 8 cm are melted together to make a new cube. 71 cm3 of the melted material is lost due to improper handling. The area of the whole surface of the newly formed cube is:
Three solid cubes of edges 4 cm, 9 cm, and 10 cm are melted together to make a new cube. If 793 cm3 of the melted material is lost due to improper handling. What is the total surface area of the newly formed cube?