Grade 10 Maths · Measurement · Use a scale factor

Use a scale factor Grade 10

Work out how a length, area or volume changes when every dimension is multiplied by a factor k, for example doubling all lengths makes the area 2^2 = 4 times and the volume 2^3 = 8 times bigger.

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Scale Factor: Enlargement and ReductionMath with Mr. Barnes

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Practice · Siyavula Grade 10 Maths · Ex 13.7 · 2 marks

If every length of a square pyramid (base edges and slant height) is a third of its original size, what will the surface area of the new square pyramid be?(2)

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More questions: use a scale factor

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3. Practice · Siyavula Grade 11 Maths · Ex 7.5 · 2 marks
The municipality intends building a cube-shaped swimming pool with volume $W^{3}$ cubic metres. It will be very expensive to fill, so they decide to make the pool smaller.
(b) Instead, the pool must stay a cube and its volume must be multiplied by a factor of $0, 8$ . Determine the new side length in terms of $W$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Set up $s^{3} = 0, 8 W^{3}$
  1 mark · Use a scale factor
2. ✓
  Side length $s = 3 0, 8 W = 0, 93 W$
  1 mark · Use a scale factor
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue
4. Practice · NavyBlue · 2 marks
A cylindrical tin has a radius of $4$ cm and a height of $10$ cm. A larger tin of the same shape has every dimension multiplied by $1, 5$ .
Use a scale factor to calculate the volume of the larger tin.(2)
Show the memo (2 ticks)Memo
1. ✓
  Scale factor $k^{3} = 1, 5^{3} = 3, 375$
  1 mark · Use a scale factor
2. ✓
  Answer $V_{large} = 3, 375 \times 160 π = 540 π = 1696, 46 cm^{3}$
  1 mark · Use a scale factor
5. Practice · NavyBlue · 2 marks
A cylinder has a radius of $3 cm$ and a height of $10 cm$ .
(b) The radius is tripled and the height is halved. By what factor does the volume change?(2)
Show the memo (2 ticks)Memo
1. ✓
  New volume $V_{new} = π (9)^{2} (5) = 405 π cm^{3}$
  1 mark · Use a scale factor
2. ✓
  Factor $\frac{405 π}{90 π} = 4, 5$
  The volume is multiplied by $4, 5$
  1 mark · Use a scale factor
6. Practice · Siyavula Grade 10 Maths · Ex 13.6 · 2 marks
If the length of every edge of a triangular prism is quadrupled, what will the volume of the new triangular prism be?(2)
Show the memo (2 ticks)Memo
1. ✓
  Scale factorEvery dimension is multiplied by $k = 4$ , so the volume is multiplied by $k^{3}$
  1 mark · Use a scale factor
2. ✓
  Answer $k^{3} = 4^{3} = 64$ : the new volume is $64$ times the original volume
  1 mark · Use a scale factor
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue

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