ID 697

A hall is cube-shaped.

The volume of the hall is 216 cubic meters.

The door is 3 meters high.

Find the length of a side of the floor.

ID 702

ID 703

ID 704

The aquarium was full of water.

A girl has tipped it on its side,

so five liters are left.

How much water does the aquarium hold when it is full of water.

ID 706

ID 707

One face of a rectangular box has an area of 15 square cm. Another face is 20 square cm and the other face is 12 square cm.

What is the height of the box?

ID 708

ID 709

This large cube is made from smaller wooden cubes.

All of the faces of the large cube are painted blue, and then it is taken apart.

What fraction of the surface is blue?

ID 713

A rectangular floor measures 3 meters by 9 meters.

It is tiled with one-square meter tiles.

Through how many tiles would the diagonal line in this rectangle pass?

ID 714

A sports club is replacing its water supply lines for a swimming pool. The current system uses two pipes, A and B, which have circular cross-sections with diameters of 6 and 8 cm, respectively. The club decides to use a single replacement pipe with the same capacity.

What is the diameter of the new pipe?

ID 715

John is building a flight of stairs.

Each stair is the same size.

What is the height of the flight of stairs X?

ID 717

ID 720

ID 721

Members of the Green Tennis Club are creating a logo.

The logo of the club is a blue square with a green shape inside.

What percentage of the logo is blue?

ID 722

Mr. Clever gave his students this pattern of gray tiles.

Develop an equation to represent the number of gray tiles, t, for any size of the inner square, n.

ID 724

ID 731

A wheel with a red mark on it is rolled along a straight line.

What is the path the mark follows during one revolution?

ID 734

ID 736

The figure consists of congruent squares.

The perimeter of the figure is 10 meters.

What is the area of the figure?

ID 739

The figure shows a regular octagon.

What is the area of the colored part as a fraction of the area of the entire octagon?

ID 750

I want to build a fence around a rectangular garden.

The garden has an area of 100 square meters.

The fence posts must be placed 1 meter apart.

What is the minimum and maximum number of fence posts needed?

ID 755

ID 760

ID 768

The bigger star is similar to the smaller one.

It is twice the height of the smaller star.

How much greater is its area?

ID 769

ID 774

ID 775

Cut 1 cube into 8 pieces. One of the pieces is a cube whose volume is three times less than that of the original cube.

What is the percentage of new surface area compared with the original cube's surface area?

ID 1005

Find two pairs of shapes that are exactly the same distance apart, where the distance between two shapes is defined as the distance between their centers.

ID 1021

You are at point A.

You can only walk to the north or east.

For example, you can go to point B by two different ways.

How many different ways are there to reach point C?

ID 1038

ID 1046

The arrow top is at the midpoint of the edge of the rectangle.

What fraction of the rectangle is shaded?

ID 1072

Each diagonal of a cube is increased by 50%.

What was the percentage increase of the volume of the cube?

ID 1082

A and B are midpoints of the corresponding sides of the rectangle.

What fraction of the rectangle is the green part?

ID 1251

ID 1260

ID 1265

ID 1373

John cuts a large piece of cheese into small pieces using straight cuts from a very sharp cheese wire.

He does not move the pieces from the original shape while he cuts the cheese.

How many rectangular pieces of cheese can he get using only five cuts?

ID 1393

All triangles are inscribed in circles with a diameter of 1 meter.

Find the triangle with the largest area.

ID 1397

ID 1461

ID 1474

Two polygons are congruent if their corresponding sides are equal in length and their corresponding angles are equal in size.

In how many ways can a regular hexagon be divided by a straight line into two congruent pentagons?

ID 1478

ID 1482

Fifteen billiard balls perfectly fit into a triangular rack.

What is the largest number of the balls that fit into the rack when its side lengths are increased by 20%?

ID 1551

I want to cut round bread into eight equal pieces.

What is the smallest number of straight cuts I can make to achieve this?

ID 1567

The diagram shows my square pond with a tree in each corner.

How much can I increase its area if I transform it into a right-angled triangle pond and keep the trees in the same place?

ID 1583

How many colored four-unit shapes can be placed inside the 6x6 square without intersecting each other?

You may turn the shape.

Find the greatest number.

ID 1595

A solid is a cube with three tunnels drilled through it, as you can see in the picture.

How many blocks are there in the solid?

ID 1599

Four matchsticks form a square.

How many non-overlapping squares can be formed using seven matchsticks?

ID 1756

Ten acrobats are evenly spaced at a circus circular arena.

Which acrobat is directly opposite the ninth performer?

ID 1792

It costs $24 to paint a cube.

Before painting, it was cut into eight cubes.

What is the cost to paint these small cubes?

ID 1793

Six shapes can be fitted together with no gaps and no overlaps to form a rectangle.

What is the smallest dimension of the rectangle?

ID 1803

I want to cut this shape into four pieces all of precisely the same size and shape.

Which is such a piece?

ID 1808

ID 1812

A rectangle floor 12 x 16 is covered by square tiles of sides 40 cm.

A chalk line is drawn from one corner to the diagonally opposite corner.

How many tiles have a chalk line segment on them?

ID 1838

ID 1847

The colored figure in the picture consists of identical isosceles right triangles.

What is the area of the blue shape?

ID 1849

ID 1868

A guard walks completely around the walls of a rectangular castle with a perimeter of 10 km.

From any point on his path, he can see exactly 1 km horizontally in all directions, except the wall.

What is the area of the region that contains all points that the guard can see during his walk?

ID 1924

In a triangle, the sum of two of the angles is equal to the third, and the lengths of the two longer sides are 17 and 15.

What is the length of the shortest side?

ID 1938

If the coordinates of one end point of a line segment are (1 , 2 , -3) and the coordinates of the midpoint are (-3 , 2, 1), what are the coordinates of the other endpoint?

ID 1951

What is the probability that a point chosen randomly from the interior of a rectangle is closer to the rectangle's center than it is to any of the rectangle's vertices?

ID 1976

Eight poles are evenly spaced on the circumference of a big circle.

What is the largest number of ropes that can be stretched between two poles so that no two ropes intersect at any point?

ID 1993

A quadrilateral with one pair of parallel sides is referred to as a trapezoid.

A trapezoid has perpendicular diagonals of lengths 4 and 6.

What is the area of the trapezoid?

ID 2043

ID 2208

ID 2280

ID 2288

ID 2290

A clock says that the time is 14:20.

The minute hand moves 300 degrees.

How many degrees has the hour hand turned?

ID 3009

ID 3010

ID 3016

ID 3017

A curtain covers a window as shown on the right.

We approximate the area of the curtain by 2 triangles.

The window is 24 by 36 inches.

How much of the window area is covered by the curtain?

ID 3023

ID 3025

ID 3030

ID 3031

ID 3032

Which figure can be rotated 72° about its center and have its final orientation appear the same as the original orientation?

ID 3033

ID 3034

In the diagram, the radii of the two concentric circles are 4.5 and 10, respectively.

What fraction of the bigger circle is shaded?

ID 3035

If two sides of the triangle have lengths of 22 and 33, which of the following could be the perimeter of the triangle?

ID 3036

ID 3041

If G is the total area of the green regular octagon and R is the total area of the red regular octagon, which is correct?

ID 3078

ID 3088

The figure shows a regular octagon.

What is the area of the colored part as a fraction of the area of the entire octagon?

ID 3102

ID 3107

ID 3116

ID 3120

ID 3121

ID 3135

In a triangle, the sum of two of the angles is equal to the third.

The lengths of the sides are 12,13 and X.

Find X.

ID 3193

ID 3212

A telephone company places round cables in round ducts.

What position of the cables is the worst and demands using the round duct with the larger diameter?

ID 3298

ID 3357

ID 3390

Anna takes a rope that is 24 ft long and creates a square.

Bob takes the rope and creates a rectangle that has an area 75% of the square's area.

What is the length of the rectangle?

ID 3663

ID 3688

ID 3716

Cut the shape into two pieces and create a square from them.

How many small squares are in the smaller of these two shapes?

ID 3770

What is the absolute difference between the largest and smallest possible areas of two rectangles that each has a perimeter of 100 units and integer side lengths?

ID 3782

Three equilateral triangles form seven unique regions.

What is the maximum number of regions that can be formed by three congruent, overlapping triangles?

ID 3936

I increase the cube so that the diagonal AB doubles its original size.

How many times does the volume increase?

ID 3990

ID 4017

I have a cube with a volume of 1000 cm^{3}.

I make the length 20% longer, the width 10% shorter and the height 10% shorter.

What is the new volume?

ID 4080

ID 4333

If we add all these vectors and place the start of the resulting vector at the origin, where does the resulting vector end?

ID 4485

ID 4502

ID 4561

If I use 30 g of batter to make a crêpe of 30 cm in diameter, how much batter do I need for a 45-cm pancake of the same thickness?

"Archaeological evidence suggests that pancakes are probably the earliest and most widespread cereal food eaten in prehistoric societies." - Wikipedia

ID 4784

ID 4874

ID 4967

James the Mathematician just measured the angle of his piece of pizza, which is 39.6°.

What part of the pizza did Gerry get?

ID 5125

A solar power station includes 17,000 mirrors, each 60m^{2}.

What is the total area of the mirrors?

1 km = 1000m

The photograph courtesy of Roland Sauter

ID 5172

Dr Heidi has been called in as an expert to solve a problem. There is a device which is spherical, air-tight when the two halves are glued together, and hollow; it is designed to be thrown into the sea and sit on the sea bed. When she asked them why they said it was hush-hush, top secret, need-to-know, ... and then they looked at her sternly. She hasn’t even seen it for herself. They said its diameter was PI (=3.1415926…) units, but they then said the units were Classified!

They said its weight is exactly 10kg. The sphere has plenty of air space inside.

What should she recommend to make the sphere sit on the sea bed?

ID 5207

Britain’s greatest inventor of mathematical puzzles Henry Ernest Dudeney asked you to place 12 mince pies in 6 lines with an equal number of pies in each line.

What is the largest possible number of pies in a line?