# Algebra - math word problems

#### Number of problems found: 3466

- Quadrilateral pyramid

In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place. - CuSO4 mixture

How many grams of solid CuSO4 we have to add to 450g of 15% CuSO4 solution to produce a 25% solution? - Two forces 3

Two forces of magnitude 8 Newtons and 15 Newtons respectively act at a point. If the resultant force is 17 Newtons, find the angle between the forces. - Intersections

Find the intersections of the function plot with coordinate axes: f (x): y = x + 3/5 - Base diagonal

In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Quadrilateral prism

The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism. - Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - A missile

A missile is fired with a speed of 100 fps in a direction 30° above the horizontal. Determine the maximum height to which it rises? Fps foot per second. - The spacecraft

The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a - Space diagonal angles

Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Quadrilateral prism

Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - Quadrilateral pyramid

The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p - Four sided prism

Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50-degree angle with the base plane. - Angle of deviation

The surface of the rotating cone is 30 cm^{2}(with circle base), its surface area is 20 cm^{2}. Calculate the deviation of the side of this cone from the plane of the base. - Pyramid 8

Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°. - Pentagonal prism

The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - Tetrahedral pyramid

Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Observer

The observer sees a straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from another end of the fence? - Square pyramid

Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side-base has an angle of 60 degrees.

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