Surafce Area And Volume Of Solid Shapes - SS1 Mathematics Past Questions and Answers - page 1

\(the\ total\ surface\ area\ of\ the\ {rubik}^{'}s\ cube = 6l^{2} = 6{(3)}^{2} = 6(9) = 54{cm}^{2}\)

\(total\ surface\ area\ of\ the\ water\ tank = (4)(3)(6)\)

\(total\ surface\ area\ of\ the\ water\ tank = (400)(300)(600)\ \) meters to centimeters

\[total\ surface\ area\ of\ the\ water\ tank = 72,000,000{cm}^{3}\]

\[capacity\ of\ water\ when\ full = \ \frac{72,000,000}{1000} = 72,000\ litres\]

\(the\ total\ surface\ area\ of\ a\ prism = sum\ of\ area\ of\ its\ sides + 2A\)

\[the\ total\ surface\ area\ of\ a\ prism = \lbrack(6 \times 5) + (6 \times 4) + (3 \times 6)\rbrack + 2(\frac{1}{2} \times 3 \times 4)\]

\[the\ total\ surface\ area\ of\ a\ prism = \lbrack 30 + 24 + 18\rbrack + 12)\]

\[the\ total\ surface\ area\ of\ a\ prism = 84{cm}^{2}\]

\(the\ volume\ of\ a\ cylinder = \ {\pi r}^{2}h\)

\(the\ volume\ of\ a\ cylinder = \ {\left( \frac{22}{7} \right)(2.5)}^{2}(7)\)

\(the\ volume\ of\ a\ cylinder = \ 137.5{cm}^{3}\)

\(capacity\ at\ three - quarter\ level = \ \frac{3}{4}(137.5) = 103.125{cm}^{3}\ or\ .103\ litres\)

\(slant\ height,\ s = \sqrt{h^{2} + r^{2}} = \ \sqrt{8^{2} + 3^{2}} = \ \sqrt{64 + 9} = \ \sqrt{73} = 8.5cm\)

\(total\ surface\ area\ = \pi rs + \pi r^{2}\)

\(total\ surface\ area\ = (\frac{22}{7})(3)(8.5) + (\frac{22}{7}){(3)}^{2}\)

\(= 80.14 + 28.29 = \ 108.43{cm}^{2}\)

\(the\ volume\ of\ a\ cone = \ \frac{1}{3}{\pi r}^{2}h\)

\(the\ volume\ of\ a\ cone = \ \frac{1}{3}{\left( \frac{22}{7} \right)(3)}^{2}(8)\)

t\(he\ volume\ of\ a\ cone = \ 75.43{cm}^{3}\)

\(the\ volume\ of\ the\ pyramids\ of\ Giza = \ \frac{1}{3}Ah\)

\(the\ volume\ of\ the\ pyramids\ of\ Giza = \ \frac{1}{3}\left( 231^{2} \right)(147) = {2,614,689m}^{3}\)