Maribel needs to add 3 ounces of sugar to a batch of cookie dough. Her sugar is

Question

Maribel needs to add 3 ounces of sugar to a batch of cookie dough. Her sugar is packaged in cubes and each cube has a volume of .25 ounces. Which of the following stacks of sugar cubes represents 3 ounces of sugar? Which set of coordinates represents a point lying on a sphere with the equation (x - 4)^2 + (y - 3)^2 + (z + 5)^2 = 25? (7, 3, -1) (4, 6, 5) (4, 3, -5) (7, 6, -1) A diameter of a sphere has endpoints (-2, 5, 0) and (4, -9, 14). What are the coordinates of the sphere's center? (-3, 7, -7) (-6, 14, -14) (2, -4, 14) (1, -2, 7) The dimensions of the first rectangle are twice as long as the dimensions of the second rectangle. How many times greater is the area of the first rectangle? 2 times 4 times 6 times 8 times

Explanation / Answer

Answer 57. (C)

Since each cube has volume = 0.25 ounces

Total volume = 3 ounces

total number of cube = 3/0.25 = 12 Nos

From the given options we have to look for cuboid that contain 12 number of cubes

Option (C) has 12 number of cubes

Option (c) is right here.

Answer 58. (A)

If any point(s) is lying on the sphere then it must satisfy given equation of sphere

Here Equation of sphere = (x-4)²+(y-3)²+(z+5)²= 25

Plug option (A) (7,3,-1) Let (x,y,z)

into given equation of sphere

(7-4)²+(3-3)² +(-1+5)²= 25

3²+0+4²=25

25 =25

Thus point A (7,3,-1) lies on the sphere.

You can check other points like but they will not satisfy above equation of shpere.

Answer 59. (D)

Since coordinates of end points of diameter od sphere is given therefore center must lies on the mid point of this diameter

Ends points coordinates are (-2,5,0) and (4,-9,14)

mid point coordinate of x = (x1+x2)/2 = (-2+4)/2 = 1

similerly mid point y = -2

similerly mid point z= 7

Coordinate of center is (1, -2,7)

Option D is correct

Answer 60. (B)

Let dimension of smaller rectangle l and b

hence dimension of larger rectangle would be 2l and 2b

Ratio of area of larger rectangle to smaller = (2l x2b)/(l x b)

Since Area of rectangle = lenght x breath

Ratio = (4lb )/(lb) = 4

area would be 4 times larger

Option B is correct

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