Bissoy.com
Doctors Medicines MCQs Q&A

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?

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? Correct Answer 2592

Given:

Length of cuboid = 12 cm

Breadth of cuboid = 54 cm

Height of the cuboid = 72 cm

It is converted into 8 cubes of the same size

Formula used:

Volume of the cuboid = lbh

Volume of cube = a3

Lateral surface area of the cube = 4a2

Calculation:

[ alt="F3 Madhuri SSC 09.05.2022 D3" src="//storage.googleapis.com/tb-img/production/22/05/F3_Madhuri_SSC_09.05.2022_D3.png" style="width: 400px; height: 114px;">

According to the question

⇒ lbh = 8 × a3

⇒ (12 × 54 × 72) = 8 × a3

⇒ (12 × 54 × 9) = a3

⇒ a3 = 5832

⇒ a = 18 cm

Now,

The sum of the lateral surface area of the two such cubes = (4a2 + 4a2)

⇒ 8a2

⇒ 8 × 18 × 18 cm2

⇒ 2592 cm2

∴ The required sum is 2592 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.
A solid metallic cuboid of dimensions 18 cm × 36 cm × 72 cm is melted and recast into 8 cubes of the same volume. What is the ratio of the total surface area of the cuboid to the sum of the lateral surface areas of all 8 cubes? 
The question below is followed by three statements I, II and III. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. What is the ratio of the volume of the cube to the volume of the cuboid? Statement I: The Total Surface Area of the cuboid is 550 cm2 and the ratio of the length, breadth and height of the cuboid is 2 : 3 : 1. Statement II: The Total Surface Area of the cube is 384 cm2. Statement III: The breadth of the cuboid is 1.5 times of the length of the cuboid and 3 times of the height of the cuboid. The difference between the height and the length of the cuboid is 5 cm.
The following questions have three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.  What is the ratio of the volume of the cube to the volume of the cuboid? I. The Total Surface Area of the cuboid is 352 cm2 and the ratio of the length, breadth and height of the cuboid is 3 : 2 : 1. II. The Total Surface Area of the cube is 726 cm2. III. The length of the cuboid is 1.5 times of the breadth of the cuboid and 3 times of the height of the cuboid. The difference between the height and the length of the cuboid is 8 cm.
What is the ratio of the volume of a cuboid to the volume of a cube? Statement I. The ratio of the height, breadth, and length of the cuboid is 1 : 2 : 3 and the total surface area of the cuboid is 352 cm2. Statement II. The total surface area of the cube is given to be 384 cm2. Statement III. The length of the cuboid is 3 times the height of the cuboid and 1.5 times the breadth of the cuboid. The difference between the length and the height of the cuboid is 8 cm.
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?
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?
“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. 
The length, breadth and height of a solid metal cuboid are 64 cm, 48 cm, and 36 cm respectively. It is melted and cut into 8 cubes of the same volume. What is the sum of the lateral surface areas (in cm2) of 3 such cubes?
Consider a cuboid with lateral surface area 18 m2 and total surface area 35.5m2 and height 1.5m. The edges of cuboid are extended such that its total surface area becomes 52 m2 and lateral surface area is 28m2 and height 2m. What is the ratio of length of cuboid in 1st case to the length of cuboid in 2nd case?