Geometry Answers

A spherical tank 4.5m in diameter contains water to a depth of 3m. Find the volume of the water. 

Find the height of a trapezoid with area of 99m2

 and the bottom base is twice the top base, 

which measures 6m.

While standing in line for the water fountain, Brian sees his lab partner 4 feet ahead of him and his best friend 7 feet to his right. Brian wants to go ask his lab partner a question, then go chat with his friend, and finally return to the water fountain line. How far will Brian have to walk in all? If necessary, round to the nearest tenth.

Each element of a circular conical pile of sand 6ft. high is inclined 45 degrees to the horizontal. How many cubic feet of sand does the pile contain?

A copper hot -water tank is in the form of a cylinder with a hemispherical cap and stands on a flat base . The internal diameter of the cylinder is 525 mm and the overall internal height is 1200 mm .

Calculate : (a) the volume of the tank in m ^ 3 (b) the capacity of the tank in litres

Draw a cuboids given by the point (6,5,2). Explain the meaning of quadric surface. Sketch the graph of x^2/4 + y^2/9 =1 in three dimensions.

5) A fruit crate has square ends and is twice as long as it is wide.

(a) Find the volume of the crate if its width is 20 inches.

(b) Find a formula for the volume V of the crate in terms of its width x.

1. A line with an angle of inclination of 45° passes through (-5/2 , -9/2). If the ordinate of the point is 6, what is its abscissa?
2. Find the angle from the line through (13/2, 0) and (2, -7) to the vertical line 5 units from the y-axis.
3. The angle from line 1 to line 2 is arctan (2/3) and the slope of line 1 is -1. Find the slope of line 2.
4. The inclination of line 1 is arctan (1/2). If line 2 makes an angle of 45° with line 1, find the slope of line 2.
5. The vertices of a triangle are (7, 4), (1, 7) and (-3, -4) Find the interior angle at the vertex (-3, -4).

An electric refrigerator is built in a form of rectangular parallelepiped. The inside dimensions are 3 ft. by 2.6 ft. by 1.8 ft. A freezing unit (1.1 ft. by 0.8 ft. by 0.7 ft.) subtracts from the storage room of the box. Find the capacity of the refrigerator.

Running from the top flagpole to a hook in the ground there is a rope that is 10 meters long. If the hook is 8 meters from the base of the flagpole, how tall is the flagpole?