Volume of a sphere: V = 3 4 π r 3 Combining dough is like combining volume. So we get V 3 = 3 4 π r 3 3 = 3 4 π r 1 3 + 3 4 π r 2 3 = 3 4 π ( r 1 3 + r 2 3 ) Where V 3 is the combined volume of dough of radii r 1 and r 2 The new radius is therefore r 3 3 = r 1 3 + r 2 3 Substituting values we get r 3 3 = 3 3 + 5 3 = 27 + 125 = 152 r 3 = 3 1 52 ≈ 5.34
So the new dough is 5.34 cm, just a bit larger.
Cylinders: V = π r 2 h So volume is directly proportional to height, if radius is constant. So ratios stay the same. 75/25=3 and the volume is also 3 times larger (ratio 3:1).
The ratio of the lengths is 75 : 25 or 3 : 1
The ratio of and area is the square of this: ie 9 : 1 or 75^2 : 25^2 (In working out the area the radius is squared)
The ratio of the volumes is the cube of this: ie 27 : 1 or 75^3 : 25^3 (In working out the volume the radius is cubed)
Hopefully this explains it
The approximate radius of the new sphere of dough formed by combining the two smaller spheres is about 5.34 cm. For the two similar cylinders, the ratio of the volume of the larger cylinder to the volume of the smaller cylinder is 27:1. This shows how volumes scale with respect to linear dimensions.
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Contoh 25 Pahlawan Nasional dengan Tanggal Lahir & Wafat 1. Ir. Soekarno – Lahir: 6 Juni 1901 · Wafat: 21 Juni 1970  2. Mohammad Hatta – Lahir: 12 Agustus 1902 · Wafat: 14 Maret 1980  3. Cut Nyak Dien – Lahir: 1848 · Wafat: 6 November 1908  4. Pangeran Diponegoro – Lahir: 11 November 1785 · Wafat: 8 Januari 1855  5. R.A. Kartini – Lahir: 21 April 1879 · Wafat: 17 September 1904  6. Tuanku Imam Bonjol – Lahir: 1772 · Wafat: 6 November 1864  7. Pattimura (Kapitan Pattimura) – Lahir: sekitar 1783 · Wafat: 16 Desember 1817  8. Sultan Agung Anyokrokusumo – Lahir: 1591 · Wafat: 1645  9. Ki Hajar Dewantara – Lahir: 2 Mei 1889 · Wafat: 28 April 1959  10. W.R. Supratman – Lahir: 9 Maret 1903 · Wafat: 17 Agustus 1938  11. Sutan Syahrir – Lahir: 5 Maret 1909 · Wafat: 9 April 1966  12. Ahmad Dahlan – Lahir: 1 Agustus 1868 · Wafat: 23 Februari 1923  13. Wahidin Sudirohusodo – Lahir: 1852 · Wafat: 1914  14. Tjut Meutia – Lahir: 1870 · Wafat: 24 Oktober 1910  15. Pangeran Antasari – Lahir: 1797 · Wafat: 11 Oktober 1862  16. Sultan Hasanuddin – Lahir: 12 Januari 1631 · Wafat: 12 Juni 1670  17. Teuku Umar – Lahir: 1854 · Wafat: 11 Februari 1899  18. Teuku Cik Di Tiro – Lahir: 1836 · Wafat: Januari 1891  19. Sisingamangaraja XII – Lahir: 1849 · Wafat: 17 Juni 1907  20. Gatot Soebroto – Lahir: 10 Oktober 1907 · Wafat: 11 Juni 1962  21. Oerip Soemohardjo – Lahir: 22 Februari 1893 · Wafat: 17 November 1948  22. Opu Daeng Risaju – Lahir: 1880 · Wafat: 10 Februari 1964  23. Kiras Bangun (Garamata) – Lahir: 1852 · Wafat: 22 Oktober 1942  24. Ali Haji – Lahir: 1808 · Wafat: 1873  25. Abdul Muis – Lahir: 1883 · Wafat: 1959