4. jūnijs - MATEMĀTIKA
EKSĀMENS 9. KLASEI
Tilpuma vienību pārveidojumi parasti sagādā grūtības.

Parasti visi zina, cik centimetri ir vienā metrā ($$1\ \mathrm{m} = 100\ \mathrm{cm}$$). Bet cik kubikcentimetri ir $$1$$ kubikmetrā?
Būtu aplami domāt, ka tikpat.

Ir jāaprēķina tāda kuba tilpums, kura katra šķautne ir $$100\ \mathrm{cm}$$ gara ($$1\ \mathrm{m} = 100\ \mathrm{cm}$$).

Svarīgi!
$1\phantom{\rule{0.147em}{0ex}}{m}^{3}=100\phantom{\rule{0.147em}{0ex}}\mathrm{cm}\cdot 100\phantom{\rule{0.147em}{0ex}}\mathrm{cm}\cdot 100\phantom{\rule{0.147em}{0ex}}\mathrm{cm}=1000\phantom{\rule{0.147em}{0ex}}000\phantom{\rule{0.147em}{0ex}}{\mathrm{cm}}^{3}$
Izpēti tilpuma vienību pārveidojumus.

$\begin{array}{l}1\phantom{\rule{0.147em}{0ex}}{m}^{3}=10\phantom{\rule{0.147em}{0ex}}\mathrm{dm}\cdot 10\phantom{\rule{0.147em}{0ex}}\mathrm{dm}\cdot 10\phantom{\rule{0.147em}{0ex}}\mathrm{dm}=1000\phantom{\rule{0.147em}{0ex}}{\mathrm{dm}}^{3}\\ \\ 1\phantom{\rule{0.147em}{0ex}}{m}^{3}=1000\phantom{\rule{0.147em}{0ex}}\mathrm{mm}\cdot 1000\phantom{\rule{0.147em}{0ex}}\mathrm{mm}\cdot 1000\phantom{\rule{0.147em}{0ex}}\mathrm{mm}=1000\phantom{\rule{0.147em}{0ex}}000\phantom{\rule{0.147em}{0ex}}000\phantom{\rule{0.147em}{0ex}}{\mathrm{mm}}^{3}\\ \\ 1\phantom{\rule{0.147em}{0ex}}{\mathrm{dm}}^{3}=10\phantom{\rule{0.147em}{0ex}}\mathrm{cm}\cdot 10\phantom{\rule{0.147em}{0ex}}\mathrm{cm}\cdot 10\phantom{\rule{0.147em}{0ex}}\mathrm{cm}\phantom{\rule{0.147em}{0ex}}=1000\phantom{\rule{0.147em}{0ex}}{\mathrm{cm}}^{3}\end{array}$

$1\phantom{\rule{0.147em}{0ex}}{\mathrm{dm}}^{3}=\frac{1}{10}\phantom{\rule{0.147em}{0ex}}m\cdot \frac{1}{10}\phantom{\rule{0.147em}{0ex}}m\cdot \frac{1}{10}\phantom{\rule{0.147em}{0ex}}m=\frac{1}{1000}\phantom{\rule{0.147em}{0ex}}{m}^{3}=0,001\phantom{\rule{0.147em}{0ex}}{m}^{3}$

$1\phantom{\rule{0.147em}{0ex}}{\mathrm{cm}}^{3}=\frac{1}{100}\phantom{\rule{0.147em}{0ex}}m\cdot \frac{1}{100}\phantom{\rule{0.147em}{0ex}}m\cdot \frac{1}{100}\phantom{\rule{0.147em}{0ex}}m=\frac{1}{1000\phantom{\rule{0.147em}{0ex}}000}\phantom{\rule{0.147em}{0ex}}{m}^{3}=0,000\phantom{\rule{0.147em}{0ex}}001\phantom{\rule{0.147em}{0ex}}{m}^{3}$

$1\phantom{\rule{0.147em}{0ex}}{\mathrm{mm}}^{3}=\frac{1}{1000}\phantom{\rule{0.147em}{0ex}}m\cdot \frac{1}{1000}\phantom{\rule{0.147em}{0ex}}m\cdot \frac{1}{1000}\phantom{\rule{0.147em}{0ex}}m=\frac{1}{1000\phantom{\rule{0.147em}{0ex}}000\phantom{\rule{0.147em}{0ex}}000}\phantom{\rule{0.147em}{0ex}}{m}^{3}=0,000\phantom{\rule{0.147em}{0ex}}000\phantom{\rule{0.147em}{0ex}}001\phantom{\rule{0.147em}{0ex}}{m}^{3}$

Dažas angļu nemetriskās tilpuma vienības:
• Akrpēda ir $$1233,48$$ ${m}^{3}$
• Kubikcolla ir $$16,39$$ ${\mathrm{cm}}^{3}$
• Naftas barels ir $$158,99$$ ${\mathrm{dm}}^{3}$
• Bušelis (ASV) ir $$35,24$$ ${\mathrm{dm}}^{3}$
• Šķidrumu galons (ASV) ir $$3,78$$ ${\mathrm{dm}}^{3}$
• Pinte ir $$0,57$$ ${\mathrm{dm}}^{3}$