What is the height of the cone below?
A cone with base of 5 inches squared and volume of 45 inches cubed.
3 in.
9 in.
27 in.
75 in.
To find the height of the cone, we can use the formula for the volume of a cone: V = (1/3) * pi * r^2 * h, where V is the volume, r is the radius of the base, and h is the height of the cone.
In this case, we are given that the base of the cone has an area of 5 inches squared, so we can find the radius by taking the square root of the base area divided by pi: r = sqrt(5/pi) ≈ 1.26 inches.
We are also given that the volume of the cone is 45 inches cubed. Plugging these values into the formula, we get:
45 = (1/3) * pi * (1.26)^2 * h
Simplifying this equation, we get:
45 = (1/3) * 1.58 * h
Dividing both sides by (1/3) * 1.58, we get:
h ≈ 45 / (1/3) * 1.58 ≈ 28.34 inches
Therefore, the height of the cone is approximately 28.34 inches. None of the given options (3 in, 9 in, 27 in, 75 in) match this result, so none of the given options is correct.
A sphere has a diameter of 10 in. What is the volume of the sphere?
V = StartFraction 125 Over 3 EndFraction inches cubed
V = StartFraction 500 Over 3 EndFraction inches cubed
V = StartFraction 500 Over 3 EndFraction pi inches cubed
V = StartFraction 4,000 Over 3 EndFraction pi inches cubed
The formula for the volume of a sphere is V = (4/3) * pi * r^3, where V is the volume and r is the radius.
In this case, the sphere has a diameter of 10 inches, so the radius is half of the diameter, which is 10 / 2 = 5 inches.
Plugging this value into the formula, we get:
V = (4/3) * pi * (5)^3
V = (4/3) * pi * 125
V = (500/3) * pi
Therefore, the volume of the sphere is (500/3) * pi inches cubed. None of the given options matches this result.
An icicle is in the shape of an inverted cone with a diameter of 11 mm and a height of 90 mm. How much frozen water is in the icicle? Use 3.14 for Pi. Round the answer to the nearest tenth.
1,036.2 millimeters cubed
1,554.3 millimeters cubed
2,849.6 millimeters cubed
4,662.9 millimeters cubed
To find the volume of the shape of an inverted cone, we can use the formula: V = (1/3) * pi * r^2 * h, where V is the volume, r is the radius of the base, and h is the height of the cone.
In this case, we are given that the diameter of the icicle is 11 mm. The radius of the base can be found by dividing the diameter by 2: r = 11 mm / 2 = 5.5 mm.
We are also given that the height of the icicle is 90 mm.
Plugging these values into the formula, we get:
V = (1/3) * 3.14 * (5.5)^2 * 90
Simplifying and calculating this expression, we get:
V ≈ 1,036.2 mm^3
Therefore, the amount of frozen water in the icicle is approximately 1,036.2 millimeters cubed, which matches option A.
Kayla says that the point labeled C in the diagram below is the center. Raymond says that point C is the radius.
A sphere. The center is C.
Who is correct and why?
Kayla is correct; the center is a fixed point in the middle of the sphere.
Kayla is correct; the center is a line segment from the center to the surface of the sphere.
Raymond is correct; the radius is the fixed point in the middle of the sphere.
Raymond is correct; the radius is a chord that is from the center to the surface of the sphere.
Kayla is correct; the center is a fixed point in the middle of the sphere.
The center of a sphere is the point that is equidistant from all points on the surface of the sphere. It is a fixed point that determines the position of the sphere. On the other hand, the radius is a line segment that connects the center of the sphere to any point on the surface. It is not a fixed point, but rather a variable distance from the center to the surface. Therefore, Kayla is correct in stating that point C is the center of the sphere.
The volume of a cone is 88 pi cubic feet. Its height is 8 feet. Fatima is finding the radius of the cone. Her work is shown below.
V = one-third pi r squared h. Step 1: 88 pi = one-third pi r squared (8). Step 2: 88 pi = StartFraction 8 Over 3 EndFraction pi r squared. Step 3: StartFraction 8 Over 3 EndFraction (88) = r squared. Step 4: 234.7 = r squared. Step 5: 15.3 = r.
What is Fatima’s error?
In step 4, Fatima did not find the correct value of StartFraction 8 Over 3 EndFraction (88).
In step 2, Fatima should not have multiplied One-third and 8.
In step 3, Fatima did not multiply 88 by the reciprocal of StartFraction 8 Over 3 EndFraction.
In step 1, Fatima did not substitute the correct value for the height in the formula.
Fatima's error is in step 2. She incorrectly multiplied one-third and 8, resulting in the equation 88 pi = (8/3) pi r squared. The correct equation should be 88 pi = (1/3) pi r squared. Therefore, the error lies in her multiplication in step 2.
To find the height of a cone, we need to use the formula for the volume of a cone. The formula is V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height.
In this case, we are given the volume of the cone, which is 45 inches cubed. Let's use this information to solve for the height.
The formula for the volume of a cone can be rearranged to solve for h:
V = (1/3)πr²h
Multiply both sides of the equation by 3 to get rid of the fraction:
3V = πr²h
Divide both sides of the equation by πr²:
h = (3V) / (πr²)
We are given that the base of the cone has an area of 5 inches squared. Since the base of a cone is a circle, we can find the radius by using the formula for the area of a circle, A = πr². Rearranging this formula, we get:
r² = A / π
r² = 5 / π
Now we have all the information we need to find the height of the cone. Let's substitute the values into the formula for h:
h = (3(45)) / (π(5 / π)²)
h = 135 / (π(25 / π))
h = 135 / (25)
h = 5.4 inches
So, the height of the cone is 5.4 inches. None of the provided options (3 in., 9 in., 27 in., 75 in.) match the correct answer.