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IPMAT Rohtak Surface Areas and Volumes — practice questions

Explore 12 free Surface Areas and Volumes questions in IPMAT Rohtak Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Surface Areas and Volumes questions and exercises with answers

Showing questions 1–12 of 12.

The distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) in 3-D isRead the answer and worked solution →In 3-D Cartesian space, the three coordinate planes are theRead the answer and worked solution →How many OCTANTS does 3-D space have, formed by the three coordinate planes?Read the answer and worked solution →The coordinates of the ORIGIN in 3-D Cartesian space areRead the answer and worked solution →The distance of the point (3, 4, 12) from the origin isRead the answer and worked solution →The distance between P(1, −3, 4) and Q(−4, 1, 2) isRead the answer and worked solution →Points P(−2, 3, 5), Q(1, 2, 3) and R(7, 0, −1) areRead the answer and worked solution →The signs of the coordinates (x, y, z) of the point (−3, 2, −1) areRead the answer and worked solution →The y-coordinate of every point on the xz-plane isRead the answer and worked solution →The midpoint of the segment joining (2, 4, 6) and (−2, 0, 4) isRead the answer and worked solution →The point on the x-axis equidistant from (1, 2, 3) and (3, 2, −1) isRead the answer and worked solution →Set of points P(x, y, z) such that PA² + PB² = 2k², with A = (3, 4, 5), B = (−1, 3, −7), tracesRead the answer and worked solution →

Worked practice questions

The distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) in 3-D is

  1. √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²)
  2. |x₂−x₁| + |y₂−y₁| + |z₂−z₁|
  3. (x₂−x₁)·(y₂−y₁)·(z₂−z₁)
  4. √(x₂² + y₂² + z₂²)
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Correct answer: A. √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²)

Extends the 2-D Pythagorean form to three coordinates. The third term inside the square root accounts for the z separation.

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In 3-D Cartesian space, the three coordinate planes are the

  1. xy-plane, yz-plane, zx-plane
  2. x-axis, y-axis, z-axis
  3. ABC plane only
  4. Cylindrical, spherical, conical planes
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Correct answer: A. xy-plane, yz-plane, zx-plane

The xy-, yz- and zx-planes are the three mutually perpendicular planes formed by pairs of coordinate axes. They divide space into 8 octants.

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How many OCTANTS does 3-D space have, formed by the three coordinate planes?

  1. 4
  2. 6
  3. 8
  4. 12
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Correct answer: C. 8

Each coordinate (x, y, z) can be positive or negative independently — 2³ = 8 octants.

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