A block of wood has the shape of a right circular cylinder with radius $6$ and height $8$, and its entire surface has been painted blue. Points $A$ and $B$ are chosen on the edge of one of the circular faces of the cylinder so that $\overset\frown{AB}$ on that face measures $120^\text{o}$. The block is then sliced in half along the plane that passes through point $A$, point $B$, and the center of the cylinder, revealing a flat, unpainted face on each half. The area of one of these unpainted faces is $a\cdot\pi + b\sqrt{c}$, where $a$, $b$, and $c$ are integers and $c$ is not divisible by the square of any prime. Find $a+b+c$.
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)
A cylindrical barrel with radius $4$ feet and height $10$ feet is full of water. A solid cube with side length $8$ feet is set into the barrel so that the diagonal of the cube is vertical. The volume of water thus displaced is $v$ cubic feet. Find $v^2$.
![](data:image/png;base64,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)
A rectangular box has width $12$ inches, length $16$ inches, and height $\frac{m}{n}$ inches, where $m$ and $n$ are relatively prime positive integers. Three faces of the box meet at a corner of the box. The center points of those three faces are the vertices of a triangle with an area of $30$ square inches. Find $m+n$.
Cube $ABCDEFGH,$ labeled as shown below, has edge length $1$ and is cut by a plane passing through vertex $D$ and the midpoints $M$ and $N$ of $\overline{AB}$ and $\overline{CG}$ respectively. The plane divides the cube into two solids. The volume of the larger of the two solids can be written in the form $\tfrac{p}{q},$ where $p$ and $q$ are relatively prime positive integers. Find $p+q.$
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)
In the accompanying figure, the outer square $S$ has side length $40$. A second square $S'$ of side length $15$ is constructed inside $S$ with the same center as $S$ and with sides parallel to those of $S$. From each midpoint of a side of $S$, segments are drawn to the two closest vertices of $S'$. The result is a four-pointed starlike figure inscribed in $S$. The star figure is cut out and then folded to form a pyramid with base $S'$. Find the volume of this pyramid.
![](data:image/png;base64,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)
A cube with side length 10 is suspended above a plane. The vertex closest to the plane is labeled $A$. The three vertices adjacent to vertex $A$ are at heights 10, 11, and 12 above the plane. The distance from vertex $A$ to the plane can be expressed as $\frac{r-\sqrt{s}}{t}$, where $r$, $s$, and $t$ are positive integers, and $r+s+t<{1000}$. Find $r+s+t$.
Let $\mathcal{R}$ be the region consisting of the set of points in the coordinate plane that satisfy both $|8 - x| + y \le 10$ and $3y - x \ge 15$. When $\mathcal{R}$ is revolved around the line whose equation is $3y - x = 15$, the volume of the resulting solid is $\frac {m\pi}{n\sqrt {p}}$, where $m$, $n$, and $p$ are positive integers, $m$ and $n$ are relatively prime, and $p$ is not divisible by the square of any prime. Find $m + n + p$.
A regular hexagon with sides of length 6 has an isosceles triangle attached to each side. Each of these triangles has two sides of length 8. The isosceles triangles are folded to make a pyramid with the hexagon as the base of the pyramid. What is the volume of the pyramid?
A $4\times 4\times h$ rectangular box contains a sphere of radius $2$ and eight smaller spheres of radius $1$. The smaller spheres are each tangent to three sides of the box, and the larger sphere is tangent to each of the smaller spheres. What is $h$?
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)
A sphere is inscribed in a truncated right circular cone as shown. The volume of the truncated cone is twice that of the sphere. What is the ratio of the radius of the bottom base of the truncated cone to the radius of the top base of the truncated cone?
![](data:image/png;base64,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)
The shape below can be folded along the dashed lines and taped together along the edges to form a three-dimensional polyhedron. All lengths in the diagram are given in inches. What is the volume of the resulting polyhedron? Express your answer in simplest radical form.
![](data:image/png;base64,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)
Distinct planes $p_1,p_2,....,p_k$ intersect the interior of a cube $Q$. Let $S$ be the union of the faces of $Q$ and let $P =\bigcup_{j=1}^{k}p_{j}$. The intersection of $P$ and $S$ consists of the union of all segments joining the midpoints of every pair of edges belonging to the same face of $Q$. What is the difference between the maximum and minimum possible values of $k$?
Jesse cuts a circular disk of radius 12, along 2 radii to form 2 sectors, one with a central angle of 120. He makes two circular cones using each sector to form the lateral surface of each cone. What is the ratio of the volume of the smaller cone to the larger cone?
The circular base of a hemisphere of radius $2$ rests on the base of a square pyramid of height $6$. The hemisphere is tangent to the other four faces of the pyramid. What is the edge-length of the base of the pyramid?
A pyramid has a square base with side of length 1 and has lateral faces that are equilateral triangles. A cube is placed within the pyramid so that one face is on the base of the pyramid and its opposite face has all its edges on the lateral faces of the pyramid. What is the volume of this cube?
A regular octahedron has side length $1$. A plane parallel to two of its opposite faces cuts the octahedron into the two congruent solids. The polygon formed by the intersection of the plane and the octahedron has area $\frac {a\sqrt {b}}{c}$, where $a$, $b$, and $c$ are positive integers, $a$ and $c$ are relatively prime, and $b$ is not divisible by the square of any prime. What is $a + b + c$?
A convex polyhedron $Q$ has vertices $V_1,V_2,\ldots,V_n$, and $100$ edges. The polyhedron is cut by planes $P_1,P_2,\ldots,P_n$ in such a way that plane $P_k$ cuts only those edges that meet at vertex $V_k$. In addition, no two planes intersect inside or on $Q$. The cuts produce $n$ pyramids and a new polyhedron $R$. How many edges does $R$ have?
What is the volume of a cube whose surface area is twice that of a cube with volume 1?
Triangle $ABC$, with sides of length $5$, $6$, and $7$, has one vertex on the positive $x$-axis, one on the positive $y$-axis, and one on the positive $z$-axis. Let $O$ be the origin. What is the volume of tetrahedron $OABC$?
A cone-shaped mountain has its base on the ocean floor and has a height of 8000 feet. The top $\frac{1}{8}$ of the volume of the mountain is above water. What is the depth of the ocean at the base of the mountain in feet?
A pyramid has a square base $ABCD$ and vertex $E$. The area of square $ABCD$ is $196$, and the areas of $\triangle ABE$ and $\triangle CDE$ are $105$ and $91$, respectively. What is the volume of the pyramid?
An aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. It is filled with water to a height of 40 cm. A brick with a rectangular base that measures 40 cm by 20 cm and a height of 10 cm is placed in the aquarium. By how many centimeters does the water rise?
Corners are sliced off a unit cube so that the six faces each become regular octagons. What is the total volume of the removed tetrahedra?
Rhombus $ABCD$, with side length $6$, is rolled to form a cylinder of volume $6$ by taping $\overline{AB}$ to $\overline{DC}$. What is $\sin(\angle ABC)$?
A unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then cut in the same manner along the dashed lines shown in Figure 2. This creates nine pieces. What is the volume of the piece that contains vertex $W$?