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Volume and Surface Area MATHS - Volume and Surface Area

Rajasthan Board (RBSE) - STD 9 - MATHS (Rajasthan - English Medium). 189 questions in this chapter.

Question types

Volume and Surface Area question types

189 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

189
Questions
5
Question groups
5
Question types
Sample Questions

Volume and Surface Area questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 Mark
The total surface area of a cube is $96\ cm^2.$ The volume of the cube is:
  • A
    $8\ cm^3$
  • B
    $27\ cm^3$
  • ✓
    $64\ cm^3$
  • D
    $512\ cm^3$

Answer: C.

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Q 2M.C.Q1 Mark
The volume of a right circular cone of height $24\ cm$ is $1232\ cm^3.$ Its curved surface area is:
  • A
    $1254\ cm^2$
  • B
    $704\ cm^2$
  • ✓
    $550\ cm^2$
  • D
    $462\ cm^2$

Answer: C.

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Q 3M.C.Q1 Mark
The diameter of the base of a cylinder is $6\ cm$ and its height is $14\ cm.$ The volume of the cylinder is:
 
  • A
    $198\ cm^3$
  • ✓
    $396\ cm^3$
  • C
    $495\ cm^3$
  • D
    $297\ cm^3 $

Answer: B.

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Q 4M.C.Q1 Mark
A beam 9m long, 40cm wide and 20cm high is made up of iron which weighs 50kg per cubic metre. The weight of the beam is:
  1. 27kg
  2. 48kg
  3. 36kg
  4. 56kg
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Q 5M.C.Q1 Mark
The length, breadth and height of a cuboid are $15\ cm, 12\ cm$ and $4.5\ cm$ respectively. Its volume is:
  • A
    $243\ cm^3$
  • B
    $405\ cm^3$
  • ✓
    $810\ cm^3$
  • D
    $603\ cm^3$

Answer: C.

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Q 72 Marks Questions2 Marks
The pillars of a temple are cylindrically shaped. Each pillar has a circular base of radius 20cm and height 10m. How much concreate mixture would be required to build 14 such pillars?
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Q 82 Marks Questions2 Marks
The outer diameter of a spherical shell is 12cm and its inner diameter is 8cm. Find the volume of metal contained in the shell. Also, find its outer surface area. $\big(\text{Take}\ \pi=\frac{22}{7}\big).$
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Q 102 Marks Questions2 Marks
A solid metallic cuboid of dimensions $(9m \times 8m \times 2m)$ is melted and recast into solid cubes of edge $2m.$ Find the number of cubes so formed.
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Q 123 Marks Question3 Marks
A spherical cannonball 28cm in diameter is melted and cast into a right circular cone mould, whose base is 35cm in diameter. Find the height of the cone.
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Q 153 Marks Question3 Marks
A circus tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105m and the slant height of the conical portion is 53m, calculate the length of the canvas 5m wide to make the required tent. $\Big(\text{Use}\ \pi=\frac{22}{7}\Big).$
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Q 165 Marks Questions5 Marks
A soft drink is available in two packs:
  1. A tin can with a rectangular base of length $5\ cm,$ breadth $4\ cm$ and height $15\ cm.$
  2. A plastic cylinder with circular base of diameter $7\ cm$ and height $10\ cm.$
Which container has greater capacity and by how much?
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Q 175 Marks Questions5 Marks
If $1\ cm^3$ of case iron weighs $21g,$ find the weight of a cast iron pipe of length $1m$ with a bore of $3\ cm$ in which the thickness of the metal is $1\ cm.$
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Q 195 Marks Questions5 Marks
A heap of wheat is in the form of a cone of diameter $9m$ and height $3.5m.$ Find its volume. How much canvas cloth is required to just cover the heap? $($Use $\pi = 3.1).$
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Q 205 Marks Questions5 Marks
A cloth having an area of $165m^2$ is shaped into the form of a conical tent of radius $5m. \Big(\text{Use}\ \pi=\frac{22}{7}\Big).$
  1. How many students can sit in the tent if a student, on an average, occupies $\frac{5}{7}\text{m}^2$ on the ground?
  2. Find the volume of the cone.
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Q 214 Marks Questions4 Marks
It costs $₹ 3300$ to paint the inner curved surface of a cylindrical vessel $10m$ deep at the rate of $₹ 30\ per\ m^2.$ Find the:
  1. Inner curved surface area of the vessel.
  2. Inner radius of the base.
  3. Capacity of the vessel.
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Q 234 Marks Questions4 Marks
A classroom is $10m$ long, $6.4m$ wide and $5m$ high. If each student be given $1.6m^2$ of the floor area, how many students can be accommodated in the room$?$ How many cubic metres of air would each student get$?$
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