All Questions ⁺⁰234663 Questions

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+1475

cylinder

The rectangle below is wrapped around a cylinder with height $10$. The rectangle perfectly covers the curved surface of the cylinder without overlap. What is the volume of the cylinder?

parmen Dec 27, 2023

Dec 26, 2023

-1

23

1

+1887

Solid

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

tomtom Dec 26, 2023

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23

1

+1887

prism

Let $ABCDEFGH$ be a rectangular prism. Find the volume of pyramid $CFAH$.

tomtom Dec 26, 2023

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16

1

+1887

pyramid

Let $ABCD$ be a regular tetrahedron. Let $E$, $F$, $G,$ $H$ be the centers of faces $BCD$, $ACD$, $ABD$, $ABC$, respectively. The volume of pyramid $DEFG$ is $18.$ Find the volume of pyramid $EFGH$

tomtom Dec 26, 2023

-1

20

1

+1887

pyramid

Let $APQRS$ be a pyramid, where the base $PQRS$ is a square. The total surface area of pyramid $APQRS$ (including the base) is $800$. Let $W$, $X$, $Y$, and $Z$ be the midpoints of $\overline{AP}$, $\overline{AQ}$, $\overline{AR}$, and $\overline{AS}$, read more ..

tomtom Dec 26, 2023

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9

1

+1887

prism

Let $PQRSTUVW$ be a rectangular prism, as shown. The area of face $TUVW$ is $10,$ the area of face $TUQP$ is $10,$ and the area of face $TPSW$ is $10.$ Find the volume of the rectangular prism.

tomtom Dec 26, 2023

0

20

1

+1887

Pyramid

Let $ABCDE$ be a right square pyramid, with base $ABCD$ and apex $E.$ Find the volume of the pyramid.

tomtom Dec 26, 2023

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32

1

+1887

prism

In the rectangular prism below, the area of face $TUVW$ is $10,$ the area of face $TUQP$ is $10,$ and the area of face $TPSW$ is $10.$ Find the volume of the rectangular prism.

tomtom Dec 26, 2023

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14

1

+1887

Cubes

Jessica has one cube with a side length of $1,$ and another cube with a side length of $1.$ She then glues the two cubes together, to form one single solid. What is the smallest possible surface area of the single solid?

tomtom Dec 26, 2023

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22

2

+1887

prism

A rectangular prism has a length of $3$, a width of $5$, and a height of $11$. What is the distance between two opposite corners of the prism?

tomtom Dec 26, 2023

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27

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+1475

Counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students read more ..

parmen Dec 26, 2023

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26

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+1475

Counting

North High School has a math club and a science club. There are a students in the math club and b students who are members of both clubs. The total number of students is c. Find an expression for the total number of students read more ..

parmen Dec 26, 2023

Dec 25, 2023

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41

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+1341

angle bisector

Let $\overline{AB}$ be a diameter of a circle, and let $C$ be a point on the circle. The angle bisector of $\angle ACB$ intersects the circle at point $M.$ Find $CM.$

kittykat Dec 25, 2023

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47

0

+1341

angle bisector

Let $\overline{AB}$ be a diameter of a circle, and let $C$ be a point on the circle such that $AC = 4$ and $BC = 4.$ The angle bisector of $\angle ACB$ intersects the circle at point $M.$ Find $CM.$

kittykat Dec 25, 2023

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35

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+1341

Circle

Let $\overline{AB}$ be a diameter of a circle, and let $C$ be a point on the circle such that $AC = 8$ and $BC = 4.5.$ The angle bisector of $\angle ACB$ intersects the circle at point $M.$ Find $\angle CMA.$

kittykat Dec 25, 2023

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