How much soil is needed to fill a rectangular hole 8 feet by 5 feet by 9 feet?
Question 4 options:
A)
200 sq ft
B)
576 sq ft
C)
405 sq ft
D)
360 sq ft
The answer cannot be determined with the given information. To calculate the amount of soil needed, we would need to know the depth of the hole.
A gelatin mold is in the shape of a hemisphere (half-sphere).
If its diameter is 2 inches, find the exact volume of gelatin that will hold.
Question 7 options:
A)
2/3π cu in.
B)
80/3π cu in.
C)
20π cu in.
D)
40/3π cu in.
The volume of a hemisphere can be calculated using the formula: V = (2/3)πr^3, where r is the radius.
Since the diameter is given as 2 inches, the radius is 1 inch.
Putting the values into the formula:
V = (2/3)π(1^3) = (2/3)π cu in.
Therefore, the exact volume of gelatin that the mold will hold is represented by option A) 2/3π cu in.
Solve the problem. Round to the nearest tenth, if necessary.
Megan drove her car 10 miles north, then made a left turn and drove 6 miles west.
How far is she, in a straight line, from her starting point?
Question 10 options:
A)
68 mi
B)
5.85 mi
C)
11.7 mi
D)
8 mi
To find the distance Megan is from her starting point, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
In this case, Megan has driven 10 miles north and 6 miles west, which forms a right triangle.
Using the Pythagorean theorem:
Distance = √(10^2 + 6^2)
= √(100 + 36)
= √136
≈ 11.66
Rounding to the nearest tenth, Megan is approximately 11.7 miles from her starting point.
Therefore, the answer is option C) 11.7 mi.
To find the amount of soil needed to fill a rectangular hole, you need to calculate the volume of the hole. The volume of a rectangular prism can be found by multiplying its length, width, and height.
In this case, the length of the hole is 8 feet, the width is 5 feet, and the height is 9 feet. Therefore, the volume of the hole is:
Volume = length x width x height
= 8 ft x 5 ft x 9 ft
= 360 cubic feet
So, the correct answer is D) 360 sq ft.
To determine the amount of soil needed to fill a rectangular hole, you need to calculate the volume of the hole. The volume of a rectangular shape can be found by multiplying its length, width, and height.
In this case, the dimensions of the hole are:
Length = 8 feet
Width = 5 feet
Height = 9 feet
To find the volume, you multiply these dimensions together:
Volume = Length x Width x Height
Volume = 8 ft x 5 ft x 9 ft
Volume = 360 cubic feet
Therefore, the correct answer is option D) 360 sq ft.