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The volume of a sphere is $36\pi$ cubic units. What is the radius of the sphere, in units? | nvidia_math | [
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-0.0... | 0.920815 | 0.879924 | 0.040891 | <think>
Alright, so I have this problem here: The volume of a sphere is 36π cubic units. I need to find the radius of the sphere. Hmm, okay. I think I remember the formula for the volume of a sphere. Let me try to recall. Is it (4/3)πr³? Yeah, that sounds right. So the volume V is equal to (4/3)π times the radius cubed... | 1 | [
{
"from": "human",
"value": "The volume of a sphere is $36\\pi$ cubic units. What is the radius of the sphere, in units?"
},
{
"from": "gpt",
"value": "<think>\nAlright, so I have this problem here: The volume of a sphere is 36π cubic units. I need to find the radius of the sphere. Hmm, okay. I ... |
A circular spinner for a game has a radius of 10 cm. The probability of winning on one spin of this spinner is $\frac{2}{5}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\pi$.
[asy]import graph;
draw(Circle((0,0),25),black);
draw((0,0)--(7,18),Arrow);
draw((0,0)--(0,25));
draw((... | tiger_math | [
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-... | 0.920414 | 0.876023 | 0.044391 | <think>
First, I recognize that the spinner is circular and has a radius of 10 cm. To find the area of the entire spinner, I'll use the formula for the area of a circle, which is π multiplied by the radius squared. So, the total area is π times 10 cm squared, which equals 100π square centimeters.
Next, the probability... | 6 | [
{
"from": "human",
"value": "A circular spinner for a game has a radius of 10 cm. The probability of winning on one spin of this spinner is $\\frac{2}{5}$. What is the area, in sq cm, of the WIN sector? Express your answer in terms of $\\pi$.\n\n[asy]import graph;\n\ndraw(Circle((0,0),25),black);\n\ndraw((0... |
A cylindrical container with a diameter of 8 inches and a height of 15 inches needs to be wrapped in a rectangular sheet of cardboard for shipping. The cardboard sheet should be large enough to completely cover the curved surface of the cylinder, and the height of the sheet should match the height of the cylinder. If t... | nvidia_math | [
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-... | 0.914088 | 0.873598 | 0.04049 | <think>
First, I need to determine the dimensions of the rectangular cardboard sheet required to wrap the cylindrical container.
The height of the cylinder is 15 inches, and this will be the height of the cardboard sheet.
Next, I'll calculate the circumference of the cylinder using its diameter. The circumference is ... | 7 | [
{
"from": "human",
"value": "A cylindrical container with a diameter of 8 inches and a height of 15 inches needs to be wrapped in a rectangular sheet of cardboard for shipping. The cardboard sheet should be large enough to completely cover the curved surface of the cylinder, and the height of the sheet shou... |
the length of a rectangle is increased by 25 % and its breadth is decreased by 20 % . what is the effect on its area ? | tiger_math | [
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-0.... | 0.938394 | 0.890463 | 0.047931 | <think>
I need to determine how changing the length and breadth of a rectangle affects its area. Let's denote the original length as L and the original breadth as B. The original area of the rectangle is then A = L × B.
When the length is increased by 25%, the new length becomes 1.25L. Similarly, when the breadth is d... | 9 | [
{
"from": "human",
"value": "the length of a rectangle is increased by 25 % and its breadth is decreased by 20 % . what is the effect on its area ?"
},
{
"from": "gpt",
"value": "<think>\nI need to determine how changing the length and breadth of a rectangle affects its area. Let's denote the or... |
A rectangular prism has a volume of 1800 cubic units. The length and width of the prism are equal, and the height is twice the length. What is the length of the prism? | tiger_math | [
0.014142158441245556,
0.01743995025753975,
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-0.0... | 0.924042 | 0.886635 | 0.037407 | <think>
First, I recognize that the volume of a rectangular prism is calculated by multiplying its length, width, and height.
Since the problem states that the length and width are equal, I'll denote the length as \( l \) and the width as \( l \) as well. The height is twice the length, so I'll represent the height as... | 10 | [
{
"from": "human",
"value": "A rectangular prism has a volume of 1800 cubic units. The length and width of the prism are equal, and the height is twice the length. What is the length of the prism?"
},
{
"from": "gpt",
"value": "<think>\nFirst, I recognize that the volume of a rectangular prism i... |
The probability it will rain on Saturday is $60\%$, and the probability it will rain on Sunday is $25\%$. If the probability of rain on a given day is independent of the weather on any other day, what is the probability it will rain on both days, expressed as a percent? | nvidia_math | [
0.004157536663115025,
0.00874430313706398,
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-... | 0.926535 | 0.865388 | 0.061148 | <think>
Alright, so I have this probability problem here. It says that the probability it will rain on Saturday is 60%, and the probability it will rain on Sunday is 25%. They also mention that the probability of rain on a given day is independent of the weather on any other day. The question is asking for the probabil... | 12 | [
{
"from": "human",
"value": "The probability it will rain on Saturday is $60\\%$, and the probability it will rain on Sunday is $25\\%$. If the probability of rain on a given day is independent of the weather on any other day, what is the probability it will rain on both days, expressed as a percent?"
},
... |
The side length of Square C is twice that of Square D. The area of Square D is $y$ square units. What is the area of Square C in terms of $y$? | tiger_math | [
0.011404966004192829,
0.017181482166051865,
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-0.018... | 0.921409 | 0.880603 | 0.040806 | <think>
To determine the area of Square C in terms of \( y \), I start by noting that Square C has a side length twice that of Square D. Since the area of Square D is \( y \), and area is calculated as the square of the side length, the side length of Square D is the square root of \( y \).
Next, the side length of Sq... | 29 | [
{
"from": "human",
"value": "The side length of Square C is twice that of Square D. The area of Square D is $y$ square units. What is the area of Square C in terms of $y$?"
},
{
"from": "gpt",
"value": "<think>\nTo determine the area of Square C in terms of \\( y \\), I start by noting that Squa... |
"the length of a rectangle is reduced by 30 % . by what % would the width have to be increased to ma(...TRUNCATED) | tiger_math | [-0.004368847236037254,0.02906154841184616,-0.050959475338459015,-0.03280529007315636,0.044447451829(...TRUNCATED) | 0.931872 | 0.892841 | 0.039032 | "<think>\nTo solve this problem, I first acknowledge that the area of a rectangle is calculated by m(...TRUNCATED) | 28 | [{"from":"human","value":"the length of a rectangle is reduced by 30 % . by what % would the width h(...TRUNCATED) |
"Given two congruent cones with a radius of 12 cm and a height of 12 cm, enclosed within a cylinder,(...TRUNCATED) | tiger_math | [0.010961344465613365,0.04163513705134392,-0.059334851801395416,-0.03196265548467636,0.0225863382220(...TRUNCATED) | 0.912708 | 0.872674 | 0.040034 | "<think>\nAlright, let me try to figure this problem out step by step. So, we have two congruent con(...TRUNCATED) | 15 | [{"from":"human","value":"Given two congruent cones with a radius of 12 cm and a height of 12 cm, en(...TRUNCATED) |
"A bag contains 10 white balls and 5 black balls. A ball is drawn at random from the bag, and if it (...TRUNCATED) | nvidia_math | [0.006048833020031452,0.02329239621758461,-0.05593585595488548,-0.02552594058215618,0.03105423040688(...TRUNCATED) | 0.940686 | 0.884677 | 0.05601 | "<think>\nOkay, let me try to figure out this probability problem. So, there's a bag with 10 white b(...TRUNCATED) | 3 | [{"from":"human","value":"A bag contains 10 white balls and 5 black balls. A ball is drawn at random(...TRUNCATED) |
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