Question

1)The formula for finding the volume of a cone is V =

1
3
πr2h. The radius of a cone is 5 cm and the height of a cone is 10 cm. What is the approximate volume of the cone?
A) 2,356 cm3
B) 52 cm3
C) 262 cm3
D) 524 cm3
2)The graph shows the dilation of quadrilateral MNOP with the origin as its center. Which rule describes this transformation?
A) (x, y) → (3x, 3y)
B) (x, y) → (x + 3, y +3)
C) (x, y) → (x - 3, y - 3)
D) (x, y) → (
1
3
x,
1
3
y)
the picture goes to #2

Answer 1

Answer: 524 cm^3

Bc i took the test

Answer 2

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=(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\\\\\\=(1)/(3)\pi r^2h\\\\\\=(1)/(3)* (22)/(7)* 5^2* 10\\\\\\=(22* 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((1)/(3)x,(1)/(3)y\right).`

Thus, (D) is the correct option.

The answers are (1). C, (2). D.