Bissoy.com
Doctors Medicines MCQs Q&A

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?

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? Correct Answer 432

Given: 

0.5  

8a3  = 0.5  

= 0.5  

8a3 = 6 × 6 × 4 × 12 

a3 = 6 × 6 × 6

a = 6

Lateral surface area of each cube = 4× 62 = 144cm2 

Lateral surface area of 3 such cubes = 3 × 144 = 432cm2  

Hint

Product of three adjacent faces & cuboid = Square of volume of same cuboid.

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.
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
Each of the six different faces of a cube has been coated with a different colour i.e., V, I, B, G, Y and O. Following information is given: i. Colours Y, O and B are on adjacent faces. ii. Colours I, G and Y are on adjacent faces. iii. Colours B, G and Y are on adjacent faces. iv. Colours O, V and B are on adjacent faces. Which is the colour of the face opposite to the face coloured with O?
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted ?
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?
A solid metallic cuboid of dimensions 12 cm × 9 cm × 16 cm is melted and recast into 216 cubes of the same size. What is the lateral surface area of two such cubes?
A solid metallic cuboid of dimensions 12 cm × 54 cm × 72 cm is melted and converted into 8 cubes of the same size. What is the sum of the lateral surface areas (in cm2) of 2 such cubes?
How many small cubes of lateral surface area 16 cm2 can be made by a cuboidal box whose length, breadth and height are in the ratio 15 ∶ 12 ∶ 8 and the lateral surface area of cuboid is 432 cm2. 
A solid cube is melted to form three solid cubes whose volumes are in the ratio of 27 : 64 : 125. Then, the sum of the total surface areas of these three solid cubes how much percentage more than the total surface area of the original cube?
A: When a sphere is cut into two equal pieces, then its total surface area is increased by 50%. B: A solid cylindrical block of volume 152 cm3 is completely dipped into a cuboidal pool of base area 19 cm2, then rise in height of water in the pool will be 8 cm. C: Inside a cuboidal box of dimension 15 cm × 24 cm × 18 cm, maximum number of small cubes of side 3 cm each that can be put will be 240. Which of the above statement(s) is/are TRUE?