Answer: The answers are (1). C, (2). D.
Step-by-step explanation: The calculations are as follows:
(1) Given that the formula for finding the volume of a cone with radius 'r' units and height 'h' units is
\(V=\dfrac{1}{3}\pi r^2h.\)
We are to find the volume of a cone with radius 5 cm and height 10 cm.
Here, radius, r = 5 cm and height, h = 10 cm.
Therefore, the volume of the cone will be
\(V\\\\\\=\dfrac{1}{3}\pi r^2h\\\\\\=\dfrac{1}{3}\times \dfrac{22}{7}\times 5^2\times 10\\\\\\=\dfrac{22\times 250}{21}\\\\\\=261.9\sim 262~\textup{cm}^3.\)
Thus, option (C) is correct.
(2) The dilation of the quadrilateral MNOP to form quadrilateral M'N'O'P' is shown in the figure.
We are to select the rule that describes the transformation.
The co-ordinates of the vertices of quadrilateral MNOP are
M(3, 3), N(9, -3), O(-6, -9) and P(-6, 6).
And the co-ordinates of the vertices of quadrilateral M'N'O'P' are
M'(1, 1), N'(3, -1), O(-2, -3) and P(-2, 2).
We see that the x-coordinate of the vertices of quadrilateral MNOP are divided by 3 to form the x-coordinates of the vertices of quadrilateral M'N'O'P'.
Similarly, the y-coordinate of the vertices of quadrilateral MNOP are divided by 3 to form the y-coordinates of the vertices of quadrilateral M'N'O'P'.
Therefore, the required transformation is
\((x,y)=\left(\dfrac{1}{3}x,\dfrac{1}{3}y\right).\)
Thus, (D) is the correct option.
The answers are (1). C, (2). D.
