(a) The curved surface areas of two cones are equal. The base radius of one is 5 cm and its slant height is 12cm. calculate the height of the second cone if its base radius is 6 cm.
(b) Given the matrices A = \(\begin{pmatrix} 2 & 5 \\ -1 & -3 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & -2 \\ 4 & 1 \end{pmatrix}\), find:
(i) BA;
(ii) the determinant of BA.
Explanation
(a) since the curved surface areas were the same, it was expected that they have 5 x 12\(pi\) = 6 \(\pi\)l and solving for the slant height to get l = 10 cm.
Then by the use of Pythagoras theorem, the height of the second cone is h\(^2\) = 10\(^2\) - 6\(^2\) and when simplified will result in h = 8 cm.
(b(i), they were to find BA = \(\begin{pmatrix} 3 & -2 \\4 & 1\end{pmatrix}\) \(\begin{pmatrix} 2 & 5 \\ -1 & -3\end{pmatrix}\) = \(\begin{pmatrix} 8 & 21 \\ 7 & 17 \end{pmatrix}\)
(b)(ii), the determinant of BA = (8 x 17) - (21 x 7) = 136 - 147 = -11