Bissoy.com
Doctors Medicines MCQs Q&A

 If a cuboid of dimensions 32 cm × 12 cm × 9 cm is cut into two cubes of same size, what will be the ratio of the total surface area of the cuboid to the total surface area of the two cubes? 

 If a cuboid of dimensions 32 cm × 12 cm × 9 cm is cut into two cubes of same size, what will be the ratio of the total surface area of the cuboid to the total surface area of the two cubes?  Correct Answer  65 : 72 

Given:

A cuboid of dimensions 32 cm × 12 cm × 9 cm is cut into two cubes of same size.

Formula used:

Volume of a cuboid = L × B × H

Volume of a cube = (side of a cube)3

Total surface area of a cuboid = 2(L × B + B × H + H × L)

Total surface area of a cube = 6 × (side)2

Calculation:

Let side of a new cube be a.

Volume of cuboid = Volume of two same cubes

⇒ 32 × 12 × 9 = 2 × a3

⇒ 1728 = a3

⇒ 12 = a

Total surface area of a cuboid = 2(32 × 12 + 12 × 9 + 9 × 32) = 2 × 12 × 65

Total surface area of a cube = 6 × 122 = 6 × 12 × 12

Required ratio =  2 × 12 × 65 : 2 × 6 × 12 × 12 = 65 : 72

∴ The ratio of the total surface area of the cuboid to the total surface area of the two cubes is 65 : 72.

 

 

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 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 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.
If a cuboid of dimensions 32 cm × 12 cm × 9 cm is melted and recast into two equal cubes of the same size, what will be the ratio of the total surface area of the cuboid to the total surface area of the two 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?
What is the total surface area of the cuboid? Statement I: The volume of the cuboid is 5184 cm3 and the ratio of the length, breadth and height of the cuboid is 3 : 4 : 2. Statement II: Total surface area of the upper and lower faces of the cuboid is 864 cm2 and the height of the cuboid is 12 cm.
If a cuboid of dimensions 16 cm × 12 cm × 8 cm is melted into three identical cubes. Then, what will be the ratio of the total surface area of the cuboid to the total surface area of the three identical cubes?
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 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?