Class 9 Measuring Space: Perimeter and Area Mock Test (CBSE)

Topics in Measuring Space: Perimeter and Area

• Perimeter of a shape
• Circumference of a circle
• Pi is irrational
• Length of an arc
• Area of a rectangle and parallelogram
• Area of a triangle
• Heron's formula
• Squaring a rectangle
• Area of a circle
• Area of a sector

Measuring Space: Perimeter and Area practice questions with answers

1. Q1Multiple choice·1 mark
   The circumference of a circle with radius $14\text{ cm}$ is (Use $\pi = \frac{22}{7}$):

   1. (a)$44\text{ cm}$
   2. (b)$88\text{ cm}$
   3. (c)$154\text{ cm}$
   4. (d)$616\text{ cm}$
   Show answer and step marks

   1. Correct option: (b) $88\text{ cm}$+1

   Answer: (b)
2. Q2Multiple choice·1 mark
   The radius of a circle is $14\text{ cm}$. Taking $\pi = \frac{22}{7}$, the area of a sector with a central angle of $90^\circ$ is:

   1. (a)$77\text{ cm}^2$
   2. (b)$154\text{ cm}^2$
   3. (c)$308\text{ cm}^2$
   4. (d)$616\text{ cm}^2$
   Show answer and step marks

   1. Correct option: (b). Area = $\frac{90^\circ}{360^\circ} \times \frac{22}{7} \times 14^2 = \frac{1}{4} \times \frac{22}{7} \times 196 = 154\text{ cm}^2$.+1

   Answer: (b)
3. Q3Multiple choice·1 mark
   If the area of a circle is $616\text{ cm}^2$, its radius is (Use $\pi = \frac{22}{7}$):

   1. (a)$7\text{ cm}$
   2. (b)$14\text{ cm}$
   3. (c)$28\text{ cm}$
   4. (d)$21\text{ cm}$
   Show answer and step marks

   1. Correct option: (b) $14\text{ cm}$+1

   Answer: (b)
4. Q4Short answer·2 marks
   A rectangular plot of land measures $18\text{ m}$ in length and $8\text{ m}$ in breadth. The owner wants a square plot having the same area as the rectangular plot, found by squaring the rectangle. Find the side of the square plot.
   Show answer and step marks

   1. Area of the rectangular plot $= \text{length} \times \text{breadth} = 18 \times 8 = 144\text{ m}^2$+1
   2. Side of the square with the same area $= \sqrt{144} = 12\text{ m}$+1

   Answer: $12\text{ m}$
5. Q5Short answer·3 marks
   A triangular plot has base $25\text{ m}$ and perpendicular height $14\text{ m}$. Find its area. A second triangular plot has the same area as the first, but its base is $35\text{ m}$. Find the perpendicular height of the second plot.
   Show answer and step marks

   1. Area of a triangle $= \frac{1}{2} \times \text{base} \times \text{height}$+1
   2. Area of first plot $= \frac{1}{2} \times 25 \times 14 = 175\text{ m}^2$+1
   3. For the second plot, $\frac{1}{2} \times 35 \times h = 175$, so $h = \frac{350}{35} = 10\text{ m}$+1

   Answer: Area of the first plot is $175\text{ m}^2$; the perpendicular height of the second plot is $10\text{ m}$.
6. Q6Short answer·3 marks
   A baker uses a round cake tin whose diameter is $14\text{ cm}$. Her assistant Ravi claims that, since the diameter is a whole number, the circumference of the tin must also be a rational number of centimetres. Is Ravi correct? Give a reason for your answer.
   Show answer and step marks

   1. Circumference $= \pi \times d = \pi \times 14 = 14\pi$ cm+1
   2. Assume $14\pi$ is rational, say $14\pi = \frac{p}{q}$ with $q \neq 0$; then $\pi = \frac{p}{14q}$, which is a rational number+1
   3. This contradicts the fact that $\pi$ is irrational, so $14\pi$ is irrational and Ravi is wrong+1

   Answer: Ravi is incorrect; the circumference $14\pi$ cm is irrational because $\pi$ is irrational.

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