(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...
Question 1 Report
(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.
Answer Details
(a) Height of the second cone. Curved surface area \(=\pi r l\).
Cone 1: \(\pi(5)(12)=60\pi\). Cone 2 has \(r=6\) and equal C.S.A.:
\(\pi(6)l_2 = 60\pi \Rightarrow l_2 = 10\text{ cm}\).
Height \(h=\sqrt{l_2^{2}-r^{2}}=\sqrt{10^{2}-6^{2}}=\sqrt{100-36}=\sqrt{64}=\mathbf{8\ cm}\).
(b) \(A=\begin{pmatrix}2&5\\-1&-3\end{pmatrix},\ B=\begin{pmatrix}3&-2\\4&1\end{pmatrix}\).
(i) \(BA\):
\(BA=\begin{pmatrix}(3)(2)+(-2)(-1)&(3)(5)+(-2)(-3)\\(4)(2)+(1)(-1)&(4)(5)+(1)(-3)\end{pmatrix}=\begin{pmatrix}8&21\\7&17\end{pmatrix}\).
(ii) Determinant of \(BA\): \((8)(17)-(21)(7)=136-147=\mathbf{-11}\).
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