Bissoy.com
Doctors Medicines MCQs Q&A

Which of the following statements is/are true? A: If the length of a cuboid is ‘x’ and its breadth and height are respectively (1/2) and (1/3) of its length, then the ratio of its surface is and its volume will be 12: x. B: If main diagonal of a cube becomes half, then the side of cube will also become half. C: If breadth of a cuboid is half of its length and it is cut into two equal pieces along the axes perpendicular to its length, then the 2 pieces formed will be cubes.

Which of the following statements is/are true? A: If the length of a cuboid is ‘x’ and its breadth and height are respectively (1/2) and (1/3) of its length, then the ratio of its surface is and its volume will be 12: x. B: If main diagonal of a cube becomes half, then the side of cube will also become half. C: If breadth of a cuboid is half of its length and it is cut into two equal pieces along the axes perpendicular to its length, then the 2 pieces formed will be cubes. Correct Answer Only A and B

CONCEPT:

Properties of cube and cuboid.

FORMULA USED:

Volume of cuboid = lbh

CALCULATION:

A: Since, length of the cuboid is ‘x’

Its breadth and height will be (x/2) and (x/3) respectively.

Now its volume will be x × (x/2) × (x/3) = x3/6 and

Its surface area will be 2 = 2x2

So, ratio between its surface are and volume is 2x2: x3/6 = 12: x.

B: Let the side of a cube is ‘a’

We know that, diagonal of the cube is ‘a√3’.

When the diagonal becomes half, then its diagonal will be ‘a√3/2’ and its side will be ‘a/2’.

C: In a cuboid the breadth is half of its length.

When it is cut into two equal pieces along the axes perpendicular to its length, the length and breadth of pieces will be equal.

In a cube: length, breadth and height should be equal, but there is no information about the height.

Hence, only A and B are true.

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 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.
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.
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 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.
The length and breadth of a cuboid is increased by 25% and 50% respectively while height is decreased by 20% and the side of a cube is decreased by 33.33%, then find the ratio of new volume of cuboid to the new volume of cube where the ratio of length, breadth, height of cuboid and side of cube is 2 : 1 : 1 : 3.
A solid cube is cut out from a solid cuboid of length, breadth are in the ratio 3 : 2 and the height of cuboid is 3 less than the breadth. If the area of four walls of cuboid is 200 cm2 then find the total surface area of the resultant solid where side length of cube is 60% of the height of the solid cuboid. 
A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height.
Two faces measuring 4 cm x 1 cm are coloured in black.
Two faces measuring 6 cm x 1 cm are coloured in red.
Two faces measuring 6 cm x 4 cm are coloured in green.
The block is divided into 6 equal cubes of side 1 cm (from 6 cm side), 4 equal cubes of side 1 cm(from 4 cm side). How many cubes will have green colour on two sides and rest of the four sides having no colour ?
“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. 
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.