(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 & 1end{pmatrix}) (begin{pmatrix} 2 & 5 \ -1 & -3end{pmatrix}) = (begin{pmatrix} 8 & 21 \ 7 & 17 end{pmatrix})
(b)(ii), the determinant of BA = (8 x 17) – (21 x 7) = 136 – 147 = -11