Geometry - practice problems - page 7 of 163
Number of problems found: 3251
- A cone 4
A cone with a radius of 10 cm is divided into two parts by drawing a plane through the midpoint of its axis parallel to its base. Compare the volumes of the two parts. - The vertices
The vertices of a triangle are A (-1,3), B (1,-1), and C (5, 1). Find the length of the median through the vertex C. - The coordinates 4
The coordinates of the vertices of ∆ABC are respectively (-4, -2), (6, 2) and (4, 6). Find the centroid G of ∆ABC. - 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? - 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? - 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? - 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. - 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 - 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. - 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. - 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. - 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 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. - 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 .
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