Geometry - practice problems - page 7 of 162
Number of problems found: 3238
- Tent - spherical cap
I have a tent in the shape of a spherical cap. Assume we want the volume to be 4 cubic meters, to sleep two or three people. Assume that the material making up the dome of the ten is twice as expensive per square as the material touching the ground. What - Plasticine cuboid
Paul makes a cuboid of plasticine with sides 5 cm, 2 cm, and 5 cm. How many such cuboids will he need to form a cube? - The Earth and Moon
The diameter of the Moon is approximately 1/4 of the diameter of the Earth. What fraction of the volume of the Earth is the volume of the Moon? - EE school boarding
Three vectors, A, B, and C, are related as follows: A/C = 2 at 120 deg, A + B = -5 + j15, C = conjugate of B. Find C. - Scale model
In a model train set, 1.38 inches represents one foot in real life. The height of One World Trade Center in New York City is 1776 feet. How tall would a scale model of the building be? Should you calculate 1776 x 1.38 or 1776 ÷ 1.38? - The centroid
The centroid of a triangle ABC is at the point (3,3,3). If the coordinates of A and B are (3, –5, 7) and (–1, 7, – 6) respectively, find the coordinates of the point C. - Prove 2
Prove that the minimum number of straight single cuts/strokes needs to divide a given right-angled triangle or an obtuse-angled triangle into a collection of all acute-angled triangles is seven(7). - Triangles - segments
How many triangles can be formed with segments measuring one and 2/3 mm one 3/4 mm and 2 1/2 mm - Freezing
A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C per hour.What will be the room temperature 12 hours after the process begins? - The temperature 39
The temperature outside is currently 10 degrees, dropping at an average rate of 2 degrees per hour. If the temperature continues to drop at this rate, what will the temperature be in 7 hours? - Iron ball 2
What is the mass of the iron ball with a diameter of 1,0 dm? The density of iron is 7870 kg/m³. . - A cube 4 A cube of edge 5 cm is cut into cubes, each of edge 1 cm. Find the ratio of the total surface area of one of the small cubes to that of the large cube.
- The radius 3
The radius of a solid circular cylinder decreases by 20% and its height increases by 10% . Find the percentage change its : (a) volume (b) curved surface area. - The temperature 38
The temperature has been dropping 2 degrees every hour, and the temperature at 10:00 AM was -15 degrees Fahrenheit. At what time was the temperature 0 degrees Fahrenheit? - Spheres - ratios
The surface area of two spheres are in the ratio 1 : 4 . Find the ratio of their volumes. - Trigonometric fx
When an acute angle φ is in the standard position, its terminal side passes through point P (1,3). Find trigonometric functions of angle θ : sin φ, cos φ, tan φ, cotan φ. - A boy 5
A boy starts at A and walks 3km east to B. He then walks 4km north to C. Find the bearing of C from A. - Building shadow
When Sun's altitude 30° above the horizontal, then find the length of the shadow of a 50 m high of a building . - Angle and slope
Find the angle between the x-axis and the line joining the points (3, -1) and (4,-2) . - Vertical components
Find the horizontal and vertical components of the vector which has magnitude 750 as shown in the following figure.
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