Let P be the cube and Q be the cuboid, such that the side of P and height of Q are in the ratio 2 ∶ 1 and the length, breadth and height of Q are in the ratio 8 ∶ 3 ∶ 6. Consider the following statements: 1. The volumes of P and Q are in the ratio 9 ∶ 1. 2. The total surface areas of P and Q are in the ratio 24 ∶ 5. Which of the above statements is/are correct?

Question

Let P be the cube and Q be the cuboid, such that the side of P and height of Q are in the ratio 2 ∶ 1 and the length, breadth and height of Q are in the ratio 8 ∶ 3 ∶ 6. Consider the following statements: 1. The volumes of P and Q are in the ratio 9 ∶ 1. 2. The total surface areas of P and Q are in the ratio 24 ∶ 5. Which of the above statements is/are correct?

Only 1
Only 2
Both 1 and 2
Neither 1 nor 2

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

Related Questions

The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements. Statements: 1) Some forces are volumes. 2) Some currents are volumes. Conclusion: I. Some volumes are forces. II. Some volumes are currents.?

1 Answers 4 Views

Consider the set of all functions f: {0,1, … ,2014} → {0,1, … ,2014} such that f(f(i))=I, for all 0 ≤ i ≤ 2014. Consider the following statements: P. For each such function it must be the case that for every i, f(i) = i Q. For each such function it must be the case that for some i, f(i) = i R. Each such function must be onto. Which one of the following is CORRECT?

1 Answers 4 Views

The total surface areas of a cube and a sphere are equal. If ‘C’ be the volume of the cube and ‘S’ be the volume of the sphere, then which of the following is correct?

1 Answers 4 Views

Which of the following statements is/are true A: If radius of a cylinder is decreased by 50% and its volume remains same, then its height will be increased by 200%. B: Difference between the curved surface area and total surface area of a cone is equal to the area of its circular base. C: If height of a cylinder is equal to its radius, then its curved surface area will be equal to the total area of its both the circular bases.?

1 Answers 4 Views

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.?

1 Answers 4 Views

If the surface areas of the three adjacent faces of a cuboid are 25%, 10% and 15% of the total surface area of the cuboid, then which of the following is a possible ratio of the length, breadth and height of the cuboid?

1 Answers 7 Views

Consider the following statements: 1. If the volume of a cylinder is 5π times the cube of its diameter, then the height of the cylinder is 20 times its radius. 2. If the curved surface area of a cylinder is 4π times the square of its diameter, then the height of the cylinder is 8 times its radius. Which of the above statements is/are correct?

1 Answers 4 Views

Which of the following statements is/are true A: If the ratio of length and breadth of a rectangle is 4 : 3 and the side of a square is equal to length of the rectangle, then the ratio of the areas of square and rectangle will be 4 : 3. B: From each corner of a rectangular sheet, if four squares of equal side are cut, then perimeter of the rectangular sheet will be decreased. C: The diagonals of a parallelogram can never perpendicular to each other.?

1 Answers 8 Views

A cuboid of breadth and height 8 cm each and length 24 cm is cut into 2 parts one of which is a cube of length 8 cm. Find the ratio of total surface area of original cuboid to that of total surface areas of two parts after cut.?

1 Answers 4 Views

A toy is made using a cuboid and a sphere. A hollow cone with outer radius 4 cm, inner radius 3 cm and height 24 cm is formed into a cuboid of length 11 cm and breadth 4 cm. Also, a hollow cylinder of thickness 2 cm, outer radius 5 cm and height 18 cm is formed into a sphere. The sphere is kept above the cuboid and toy is made. Which of the following is true?

1 Answers 4 Views

AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : Only 2

Given,

Ratio of side of P & height of Q = 2 ∶ 1

Ratio of length, breadth & height of Q = 8 ∶ 3 ∶ 6

Let,

Length of Q = 8x

Breadth of Q = 3x

Height of Q = 6x

⇒ Side of P = 2 × Height of Q = 12x

Considering statement 1,

Volume of cube = (side)³

Volume of cuboid = Length × Breadth × Height

⇒ Volume of P/Volume of Q = (12x)³/(8x × 3x × 6x) = 12

⇒ Volume of P∶ Volume of Q = 12 ∶ 1

Hence, statement 1 is not correct

Considering statement 2,

Total surface area of cube = 6 (side)²

Total surface area of cuboid = 2 (Length × Breadth + Breadth × Height + Height × Length)

⇒ Total surface area of P/Total surface area of Q = / = 864x²/180x² = 24/5

⇒ Total surface area of P∶ Total surface area of Q = 24 ∶ 5

Hence, statement 2 is correct

∴ Only statement 2 is correct