Geometry - math word problems
Number of problems found: 1340
- Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
Openings in perforated bricks occupy 10% and brick has dimensions 30 cm, 15 cm and 7.5 cm. Calculate a) the weight of a perforated bricks, if you know that the density of the full brick material is p = 1800 kg/m3 (1.8 kg/dm3) b) the number of perforated
- Three glasses
Three glasses of different colors have different volumes. Red 1.5 liter is filled from 2/5, blue 3/4 liter is filled from 1/3, and the third green 1.2 liter is empty. Pour green glass 1/4 of the contents from the red glass and 2/5 of the content from the
- Two cylinders
Two cylinders are there one with oil and one with an empty oil cylinder has no fixed value assume infinitely. We are pumping out the oil into an empty cylinder having radius =1 cm height=3 cm rate of pumping oil is 9 cubic centimeters per sec and we are p
- Orlík hydroelectric plant
The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the p
Before Christmas, Eva bought two cylindrical candles - red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 p. M. , lit a green candle at 7:00 p. M. , and left them both on fire until they burned. At 9:30 p. M. , bo
- Cardboard box
Peter had square cardboard. The length of the pages was an integer in decimetres. He cut four squares with a side of 3 dm from the corners and made a box out of it, which fit exactly 108 cubes with an edge 1 dm long. Julia cut four squares with a side of
- Truncated cone
Calculate the height of the rotating truncated cone with volume V = 794 cm3 and a base radii r1 = 9.9 cm and r2 = 9.8 cm.
- Angled cyclist turn
The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
- Mouse Hryzka
Mouse Hryzka found 27 identical cubes of cheese. She first put in a large cube out of them and then waited for a while before the cheese cubes stuck together. Then from every wall of the big cube she will eats the middle cube. Then she also eats the cube
The pit has the shape of a truncated pyramid with a rectangular base and is 0.8 m deep. The pit's length and width are the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of the pit we use 0.6 l of green color. How many liters of paint are nee
- Equilateral cone
We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down?
- Wooden block
A cuboid-shaped wooden block has 6 cm length, 4 cm breadth, and 1 cm height. Two faces measuring 4 cm x 1 cm are colored in black. Two faces measuring 6 cm x 1 cm are colored in red. Two faces measuring 6 cm x 4 cm are colored in green. The block is divid
- Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
- Brick wall
Garden 70 m long and 48 m wide should surround with wall 2.1 meters high and 30 cm thick. Wall will be built on the garden ground. How many will we need bricks if to 1 m³ is required approximately 300 bricks?
- Eq2 2
Solve following equation with quadratic members and rational function: (x2+1)/(x-4) + (x2-1)/(x+3) = 23
- Total displacement
Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back t
- Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this
- Rhombus construction
Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...
- Four prisms
Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm2 b) 300 cm2 c) 3000 cm3 d) 300 cm3 Question No.2: The base of the prism is a rhombus with a side length of 30 cm and a height of 27 cm. The heig