Length

7 Grade 7 Mathematics questions on Length, with worked marking schemes. 7 questions are available on this topic in full.

1. Question 1

   4 marks

   Find the circumference and area of a circle with radius 21 cm. (Use $\pi =\frac{22}{7}$)

   (4 marks)

   Marking scheme

   The circumference of a circle is $2\pi r$. With $r=21$ cm: $2\times \frac{22}{7}\times 21$. (1)

   $\frac{22}{7}\times 21=66$, so the circumference is $2\times 66=132$ cm. (1)

   The area is $\pi r^2$, and $21^2=441$. (1)

   $\frac{22}{7}\times 441=22\times 63=1,386$. (1)

   Final answer: the circumference is $132$ cm and the area is $1,386$ cm${}^2$.

2. Question 2

   1 mark

   A semicircular region has diameter 28 cm. What is the perimeter? (Use $\pi =\frac{22}{7}$)

   A. 56 cm

   B. 72 cm

   C. 88 cm

   D. 44 cm

   (1 mark)

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3. Question 3

   1 mark

   Convert 3.75 km to cm.

   A. 3,750,000

   B. 375,000

   C. 3,750

   D. 37,500

   (1 mark)

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4. Question 4

   1 mark

   The perimeter of a regular hexagon is 54 cm. What is one side?

   A. 9 cm

   B. 12 cm

   C. 6 cm

   D. 27 cm

   (1 mark)

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5. Question 5

   3 marks

   The arc length of a sector is 22 cm and the radius is 21 cm. Find the angle of the sector. (Use $\pi =\frac{22}{7}$)

   (3 marks)

   Marking scheme

   The arc is the fraction $\frac{\theta }{360}$ of the whole circumference: arc $=\frac{\theta }{360}\times 2\pi r$. (1)

   The circumference is $2\times \frac{22}{7}\times 21=132$ cm, so $22=\frac{\theta }{360}\times 132$. (1)

   Multiply both sides by $360$ and divide by $132$: $\theta =\frac{22\times 360}{132}=60$. (1)

   Final answer: $60^{\circ }$.

6. Question 6

   1 mark

   The circumference of a circle with diameter 14 cm is: (Use $\pi =\frac{22}{7}$)

   A. 154 cm

   B. 22 cm

   C. 88 cm

   D. 44 cm

   (1 mark)

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7. Question 7

   4 marks

   A running track is made of two straight sections of 100 m each and two semicircles of diameter 56 m. Find the total length. (Use $\pi =\frac{22}{7}$)

   (4 marks)

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