Question
Manoj has a set of blocks that are of the same height. The cone shaped block has a volume of 125 cubic inches. The sphere-shaped block has a volume of 250 cubic inches. What do you know about the radius of the base cone – shaped block?
Hint:
Since the blocks are of same height, the height of sphere-shaped block is the diameter of the block. So, the diameter of sphere block is equal to the height of cone block. Then we form two equations using the given information and solve the system of equations.
The correct answer is: The radius of the cone shaped block is (35156.25/π^2 )^(1/6).
Explanations:
Step 1 of 2:
Volume of cone shaped block =
, r = base radius and h = height
Volume of sphere-shaped block =
, h = diameter of the block
Given,![4 over 3 pi open parentheses h over 2 close parentheses cubed equals 250](data:image/png;base64,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)
![not stretchy rightwards double arrow h cubed equals 1500 over pi](data:image/png;base64,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)
Step 2 of 2:
Also given, ![1 third pi r squared h equals 125](data:image/png;base64,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)
![not stretchy rightwards double arrow 1 over 27 pi cubed r to the power of 6 h cubed equals 125 cubed comma text taking cube on both sides end text](data:image/png;base64,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)
![not stretchy rightwards double arrow r to the power of 6 equals 125 cubed cross times 27 cross times 1 over pi cubed cross times pi over 1500 comma text putting end text h cubed equals 1500 over pi](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYkAAAAmCAYAAAAx4GcyAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAB5tJREFUeNrtnV9kH1kUx4+IVREh9qGqolSsWivKqhXVh7xEVESEiBW1YonVhxVr6UPVPlRZa62KChURKypErBW1SlVF9SGsqNqHVaL2IVaUPKyI+Pnx23v8zvhNJndm7tz5d+f3+344ZOZ383Nn5p5z7jlz7/kRAVAOnyi5p+QNbgWAHoTqQSNCgvQpWVKyI/JYztm2A6BU1pTMhwx2AKAHLSdhygslE77jcTln2w4AJ4CTACC9k5hWsqg5/1DJlxbtAICTAKCNnMSmklHN+RH5LGk7AOAkcuK2kmOKziXfwWMHGTuJQyUfac7zuQOLdgDASeTEr0oGZFY2GZjBjeNxAwsnUVPyn5I/lHynpFfTrh7x3TWLdgDASeTMnjgLj/dKzuNxA0s96FbyOTVXQv2t5EoCJ3Fi0c4JvlCyLR1rtJGxaPi8Py9rG8X47zgnwQp9HDg+wqOGzmakB6NiO/1wqkiXRjpHp9NIpu1K51Mlu0o+a/PBx97+H+hgxzmJYSUvA8dYYgidzVIPgrN+TmeOhTiUTYt2pcN52xsdMOC6qPmiCHSWk+ClhKu+4xkZ8wA6m4Ue8OR6L3BuSsmypu0qnV7aatqudD4omRWP/Y6aa3fbjY+VPFIyB73rOCexFHju92UsAOhsUj34TSLRLpExcRBTmrYcvS5QM73JKaW7dDYtlaRdqdTFm/VJJ5dzfDBx296vS5jFqwe8nORsyEM03R7vnb+V0zVl0eeyjbNr/ckSVuKrvuMHSp4rGVTSg8lAoRyLcTUdj7cc04NpmUjXJcLZUHIt5Lv6laxQMxXF183lNnpTtCuVd4EH10v55QHjtr1vS5jl3SR+X/JaE3olHeR9Yhzmc7gm0z6HMR0ScoL08LLX3cC5a+LQ19rkGg8Tni/LSbBTfuuIzoKELIs38+Bo4k+HZjKXNIPLdpAXtazskqFC8DLMV9RczQBAlrrkWjTIDnvdYZ1tS74n82qBP1BzZ+k34gBOqLXTdIiaL/L4uzgvxnnAMcfC3ZMMFOBGjPO7K5L0szSDeyuQCsm7T0VR1X4XZdSHJALl9OS/1NyUZWP8w1IjJilY3TFHtXsydrl/A5r/HfbZEG47Z6iPng3idw2/UHOJJ0c736bQWWCgiJwWum7QlnNn+0p+VnJZ8/msPPADin5x3aBscutJjDwPyteW/+/1iQf0M5nhJzVuNkZN1+cg7LDvWRrcKhjaqva7CCfBY4N3fHOa9wIlS6k2MogkdN/Bev+TT0fm6OwL1CtiJ7zVkGxLnhjq44Y4Co6cJ+TaL4pu9ljqbFb2qPIDykQeUPQLIX7vMFWBEDkIp2F2NI7QdHt8WuNmY9TC+uznkrTpLqhPLjgKOIjW2O3XTCq2S3YSI4FzXXS2NAQvzZy31Ge2QU81enoo0QXIkRV5SE9CPueHfeygosTBivQ7Re+4jNsen8a4PbcwaiZ9JjEIIzn3qVGAVLXfRd+DuLGv09GinYRJuw8aB2eiz3x9R3R2NVl3ibapbcaZ6Rf8GBFJcMmNlwXe2CycxGUxtoMJ+qbbHl+kkzDt87REP0U5LheiiSr2u+gJUq0CTsL2JTnbIN0u9+GUtgnpJgPlM3knEdxx6nokwdHAMtmtYT/J6L4mTZGY9rlLIp6rHZK2QbrJbOzzisL9CjiJsH0OccY4zAa5aJvaCl7dZJKH518++roiToKXhG6Qea7ej257fBqjRobGLUmfJy2iHby4bn8nwaVCVgLn6hqDvKj5/1qI4a5FZBdsncQzmf376TdwEtzvuYrYpo6Et5LfrIiTeEpm7xWSbI9PY9RMPjPtM7NOyXazYwlstViXsT0ZM/a3qFVQc0iiy2CakicTX8nfgzIRmdHozhvSb9wMO5/GSbAdeSUTI0/vdgwi+DAb5KJt6kh49YArm7XicoamucUk2+PLuKawfOgB6V/8uTrjRZn1fJzEnExqePzyjnBdgc0Bau2leOGbwQfH1YiMK9PzaZwEycx/X/q1Q60d7DY2yCXbBABIQdll1uNqfiVx1LxpdEkMHMtj0m9KNW2ncxQ3LaLoqnKeUHodgI6n7DLrcTW/khheNmgTvuPxECNn2s4PL0j4i6LfT1XdSWz5ovYLcozqygB0MC6VWU/rJDhNuag5/5BO5+9N2wW5SPE/i1r1WkR8b95SqyzHAlQEgM6lrJLNeTkJLumue7cyQmd/McykHQDMbWouD45Ke97BbQLtikslm9M6CU6Z6X5TmM8dWLQDgOECqQMygZgMTDbGcXtAp+BCmiTKSZjU8qpHfHfNoh0AfvbodOXc9xSffgSgLcJiV0o2x0UMcbW86oZO0LQdAP6xdxw4PsJtAe0cFicts+6Ck/Cjq+XFqSJdGukcnU4jmbYDwCNYh4qPsTQYICx22EnoZv3sDMdCHMqmRTsAPIJ1qGZkUgYAwmJHnYSulheXbdH9nvgqnV7aatoOAA/eeOlfJn6fmkvHAUBY7ICTSFLLi699QZwjp5S4jtR2inYAeNG5v7ozrwjkEvlcd6sHtwcgLM7fOWRVy4trZ3HF1ROJqLjcRm+KdgDw+73dwDmvptUabg9AWAwAAABhMQAAAITFAABH+R+75mRw5UyN3gAAAdZ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3gyMUQyOzwvbW8+PG1zdXA+PG1pPnI8L21pPjxtbj42PC9tbj48L21zdXA+PG1vPj08L21vPjxtc3VwPjxtbj4xMjU8L21uPjxtbj4zPC9tbj48L21zdXA+PG1vPiYjeEQ3OzwvbW8+PG1uPjI3PC9tbj48bW8+JiN4RDc7PC9tbz48bWZyYWM+PG1uPjE8L21uPjxtc3VwPjxtaT4mI3gzQzA7PC9taT48bW4+MzwvbW4+PC9tc3VwPjwvbWZyYWM+PG1vPiYjeEQ3OzwvbW8+PG1mcmFjPjxtaT4mI3gzQzA7PC9taT48bW4+MTUwMDwvbW4+PC9tZnJhYz48bW8+LDwvbW8+PG10ZXh0PiYjeEEwO3B1dHRpbmcmI3hBMDs8L210ZXh0Pjxtc3VwPjxtaT5oPC9taT48bW4+MzwvbW4+PC9tc3VwPjxtbz49PC9tbz48bWZyYWM+PG1uPjE1MDA8L21uPjxtaT4mI3gzQzA7PC9taT48L21mcmFjPjwvbWF0aD5gyMCrAAAAAElFTkSuQmCC)
![not stretchy rightwards double arrow r to the power of 6 equals fraction numerator 35156.25 over denominator pi squared end fraction](data:image/png;base64,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)
![not stretchy rightwards double arrow r equals open parentheses fraction numerator 35156.25 over denominator pi squared end fraction close parentheses to the power of 1 divided by 6 end exponent](data:image/png;base64,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)
Final Answer:
The radius of the cone shaped block is
.
Related Questions to study
The slope of a line is –½ and it passes through origin. Find its equation.
The slope of a line is –½ and it passes through origin. Find its equation.
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The graph shows the subscription cost to a certain club in town. Write an equation of the
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Find a value for k so that the line through (k, 6) and (4, 2) is perpendicular to the line with equation x + 2y = 2.
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Find a value for k so that the line through (35, k) and (42, 27) is parallel to the line with equation y = x.
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Find the equation of line such that its y-intercept is 20 and slope is ½.
A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis?
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The difference between the sides at right angles in right angled triangle is 14 cm. The area of triangle is 120 cm2 . Calculate the perimeter of triangle
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The ratio of the diameter and height of a cylinder is 4 : 5. Find the height of the cylinder, if its volume is 540π cubic units.
The ratio of the diameter and height of a cylinder is 4 : 5. Find the height of the cylinder, if its volume is 540π cubic units.
Identify the parallel lines and perpendicular lines from the given set.
2x + y = 1
9x + 3y = 6
y = 3x
y = -3x
2y = 4x +6
Y = - x/2
Identify the parallel lines and perpendicular lines from the given set.
2x + y = 1
9x + 3y = 6
y = 3x
y = -3x
2y = 4x +6
Y = - x/2
![](data:image/png;base64,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)
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is
greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?
Note:
There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).
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)
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is
greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?
Note:
There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).
Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.
Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.
Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.
¶A line's slope can be determined using its two points (x1, y1) and (x2, y2). The formula (y2 - y1) / is used to find the change in y and divided by the change in x. (x2 - x1).
Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.
Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.
Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.
¶A line's slope can be determined using its two points (x1, y1) and (x2, y2). The formula (y2 - y1) / is used to find the change in y and divided by the change in x. (x2 - x1).
Write the equations of the given lines.
Line 1: y-intercept = 3, slope = 2
Line 2: y-intercept = - 1, slope = -5
Write the equations of the given lines.
Line 1: y-intercept = 3, slope = 2
Line 2: y-intercept = - 1, slope = -5
![](data:image/png;base64,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)
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?
Note:
A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.
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)
Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?
Note:
A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.