ID 853

A rectangle has a width of 0.3x and a length of 0.4x.

Which formula is the correct one to calculate the perimeter (P) in terms of x?

ID 854

ID 858

The edges of a large cube are 3 times longer than the edges of a small cube.

How many times greater is the volume of the large cube than the small cube?

ID 863

ID 868

Two satellites orbit at 1/4 R above Earth's surface. R is the radius of the Earth.

What is the maximum distance at which the two satellites can see each other?

ID 869

A mathematician wants to approximate the width of a lake.

He places 5 markers near the lake and measures the distances shown in the diagram.

What is the width of the lake in meters (m) from point P to point Q?

ID 870

ID 872

ID 873

ID 874

ID 878

A square garden is 401 square meters.

The minimum distance between apple trees is 5 meters. The minimum distance between a tree and the fence around the garden is 5 meters.

How many trees are there?

ID 879

ID 882

A boy is making boxes from cardboard.

He is going to cut square pieces off each corner as shown in the diagram and fold the sides up.

Which size of square pieces would give a larger box in terms of volume?

ID 884

ID 889

ID 896

Five boys Andrew, Brandon, Chris, Daniel, and Ethan live on State Street.

At which point should the children meet so that the sum of the distances they walk to that point is minimized?

ID 897

A boy cuts a cardboard circle and only cuts 5 straight lines.

He does not care if the pieces are equal.

What is the maximum number of pieces he can obtain if he makes 5 cuts without moving the cut pieces?

ID 898

ID 904

ID 905

The figure shows a pyramid made of small squares.

I want to move the small squares and transform the pyramid into a big square.

What is the lowest possible number of moves that need to be made?

ID 915

The American flag consists of thirteen equally spaced, horizontal red and white stripes, with a blue rectangle in the canton bearing fifty small, white, five-pointed stars.

What part of the flag is red?

ID 919

ID 988

Divide the analog watch face with two straight lines so that the sums of the numbers in each part are equal.

Which is true?

ID 1013

Look at the mini-golf course.

To what point would the player hit the golf ball to make a hole-in-one?

ID 1032

ID 1042

Bill mows the front lawn, which is a 7m by 10m rectangle.

The mower cuts a 1m wide strip.

If Bill starts at the corner and mows around the lawn in a spiral toward the center, how many times around must he go before he has mowed the lawn?

ID 1075

ID 1223

A block of wood in the form of a cuboid 9 x 10 x 11 has all its six faces painted red.

If the wooden block is cut into small cubes of 1 x 1 x 1, how many of these cubes would have red paint on them?

ID 1250

I fold a square piece of paper in half four times without unfolding, making an isosceles right triangle each time.

What is the correct net of the creases on the paper after unfolding the paper?

ID 1252

ID 1253

ID 1259

Path C consists of straight segments.

Path D and E consist of semi-circles.

Which path is the longest?

ID 1279

A circle is drawn through two vertices of a square so that it is tangent to one side of the square.

The square has sides of length 8.

Find the radius of the circle.

ID 1352

I placed together four identical triangles and the square, without overlaps, to form a figure.

What is the least possible perimeter of the new figure?

ID 1353

ID 1398

ID 1401

Eight points are equally spaced on a circle.

How many right angled triangles that have all their vertices at three of these points can you draw?

ID 1444

The picture shows six equilateral triangles.

The sides of the triangles are three times longer than are the side of the regular hexagon.

What fraction of the whole shape is blue?

ID 1462

The picture shows a tiling pattern which is made of square green tiles 10 x 10 cm and gray tiles 20 x 10 cm.

The pattern is extended to cover a large surface.

What fraction of the surface is colored green?

ID 1483

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 decreased by 20%?

ID 1487

What is the smallest number of segments that needs to be moved so that the pattern has a line of symmetry?

ID 1526

All three circles are tangent to the horizontal line and to one another.

The diameter of the small circle is 2.

Find the diameter of the big circles.

ID 1578

A girl wants to cut the paper into several equal pieces of the same shape, and with nothing left over.

(NOTE: She does not have to cut along the dotted lines.)

How many pieces are possible?

ID 1755

Two lines and two diagonals are drawn through the center of the rectangle.

What fraction of the area of the rectangle is green?

ID 1807

ID 1811

I would like to cut the shape into the fewest possible pieces that will fit together and form a rectangle.

What is the smallest number of pieces?

ID 1848

The colored figure at the picture consists of isosceles right triangles.

What is the largest possible area of the blue shape?

ID 1865

The vertices of the smaller square divide each side of the larger square by a ratio of 2:1.

What fraction of the larger square is blue?

ID 1966

I blew some air into a spherical balloon and quadrupled its surface area (4 times).

By how much did I multiply the volume of the sphere?

ID 1977

ID 2158

Four matchsticks form a square.

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

Note: The matchsticks do not intersect each other.

ID 2186

ID 2188

What is the maximum number of apples (ideal spherical units) that can touch another given apple (spherical unit) without overlapping?

ID 2200

I arranged twelve one-inch wooden sticks in a polygon with an area of 6 square inches.

I would like to form a polygon with an area of 4 square inches using these 12 sticks.

What is the minimum number of sides of the new polygon?

ID 3113

ID 3114

Anna has made puzzle pieces by cutting wedges from a disk.

Each wedge cut from the disk has a 50-degree angle at the center of the disk.

The weight of the uncut disk is 108 grams.

How many grams does each 50-degree wedge weigh?

ID 3115

How many coins do I need to melt down and recast to get a single coin of double thickness and double diameter?

ID 3123

Shape A and B are congruent equilateral triangles.

Shape C is formed by superimposing shapes A and B by about their centers.

What is the perimeter of shape C if the perimeter of shape A is 45 inches?

ID 3124

The diagram illustrates a row of three squares formed by matches.

How many matches will it take to make a row of 33 squares?

ID 3162

A boy stacked colored cubes in a square pyramid like the one shown here.

The top layer had 1 cube, the second layer had 4 cubes, and so on.

If the pyramid were 16 layers high, how many cubes would be in the sixteenth layer?

ID 3163

The figure shows a red equilateral triangle inscribed within another equilateral triangle. The side of the bigger triangle measures 10 meters.

What is the ratio of blue area to the total area of the largest triangle?

ID 3168

The three circles have fixed centers, and the diameter of a circle is 7 / 8 of its 'left neighbor'.

The left circle completes a hundred revolutions per minute.

Estimate how many revolutions the right circle completes.

ID 3173

ID 3174

Two similar pyramids have volumes of 343 m^{3} and 64 m^{3}.

What is the ratio of their surface areas?

ID 3224

ID 3651

ID 3762

Squares 1, 2 and 3 have sides of length 1, 2 and 3 units, respectively.

What is the perimeter of the entire figure if there are 100 such squares in the shape?

ID 3791

A square with a side length 20 has two vertices on the circle, and one side touching the circle.

Find the diameter of the circle.

ID 3928

Two squares, each with sides measuring 2 cm, are placed such that a vertex of one lies at the center of the other.

What is the area of the overlapping region?

ID 3934

A recipe makes 5 pizzas that are 12 inches in diameter.

If I decide to make 3-inch diameter pizzas, how many of the smaller pizzas would this recipe make?

ID 3935

Two congruent circles share a radius.

What is the perimeter of the figure compared with the perimeter of the original circle?

ID 3951

ID 3966

ID 4013

ID 4049

ID 4075

What is the largest possible side size of an equilateral triangle that fits into a square with a side size 10?

ID 4166

The hypotenuse of a right triangle is 6, and the length of one leg is 2 units longer than the length of the other.

Whatâ€™s the area of the triangle?

ID 4231

What part of the rectangle is red if points A and B are the midpoints of the corresponding sides of the rectangle?

ID 4325

ID 4427

Three overlapping squares form 5 squares including themselves in the picture.

What is the greatest number of squares you can make by overlapping three squares of the same size?

ID 4430

You have a 5kg weight and a 12kg weight.

They are the same height and are made from the same material.

What is the ratio of their diameters?

ID 4714

Estimate the maximum number of smaller 1-inch circles that fit in a larger circle, the diameter of which is 2.9 times larger.

ID 4863

What is the volume in cubic inches of the pyramid with height 10 inches?

The pyramid consists of equal cubes.

ID 5039

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

How many sides do the four pieces have?

ID 5051

ID 5115

ID 5160

ID 5304