Similar Solids (VCE SSCE General Mathematics): Quizzes

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Similar Solids
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What two conditions must solids meet to be similar?

Same shape & equal dimension ratios

If linear dimensions are multiplied by kk, the volume is multiplied by what?

k3k^3

If you double all dimensions of a solid (k=2k = 2), the volume becomes how many times larger?

88 times

Cuboid A is 99 cm × 66 cm × 33 cm. Cuboid B is 33 cm × 22 cm × 11 cm. Are they similar?

Yes, all ratios equal 13\frac{1}{3}

If linear scale factor is k=13k = \frac{1}{3}, what is the volume scale factor?

127\frac{1}{27}

Two similar cylinders have radii 22 cm and 11 cm. What is the linear scale factor kk?

12\frac{1}{2}

Two similar cones have linear scale factor k=4k = 4. What is the volume scale factor?

6464

A solid has dimensions 33 times those of a similar solid. How many times larger is the volume?

2727 times

A solid has dimensions 77 times a smaller similar solid. What is the volume ratio?

343343 times larger

To verify two solids are similar, what must you check about corresponding dimensions?

All ratios must be equal

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