# Expression of a variable from the formula - 9th grade (14y) - math problems

#### Number of problems found: 540

- Trapezoid 25

Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s. - Sphere cut

A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the volume of the segment. What is the distance of the cutting plane from the center of the sphere? - Ladder

How long is a ladder that touches on a wall 4 meters high and its lower part is 3 meters away from the wall? - Railway embankment

The section of the railway embankment is an isosceles trapezoid, the sizes of the bases of which are in the ratio 5: 3. The arms have a length of 5 m and the height of the embankment is 4.8 m. Calculates the size of the embankment section area. - The pyramid

The pyramid with a square base is 50 m high and the height of the sidewall is 80 m. Find the endge of the base of the pyramid. - Vertical rod

The vertical one meter long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time. - Sphere in cone

A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele - Triple and quadruple rooms

Up to 48 rooms, some of which are triple and some quadruple, accommodated 173 people so that all beds are occupied. How many triple and how many quadruple rooms were there? - 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? - Powerplant chimney

From the window of the building at a height of 7.5 m, the top of the factory chimney can be seen at an altitude angle of 76° 30 ′. The base of the chimney can be seen from the same place at a depth angle of 5° 50 ′. How tall is the chimney? - Chord of triangle

If the whole chord of the triangle is 14.4 cm long, how do you calculate the shorter and longer part? - Coils of transformer

The primary coil of the transformer has 1100 turns and is connected to a voltage of 220V. How many turns does the secondary coil have when the voltage on it is 55 V? Determine the transformation ratio and decide what kind of transformation is it. - Coils of transformer

The primary coil of the transformer has 400 turns, a current of 1.5 A passes through it and is connected to a voltage of 220 V. For the secondary coil, find the voltage, current, and a number of turns if the transformation ratio k = 0.1. - The cylinder

The cylinder has a surface area of 300 square meters, while the height of the cylinder is 12 m. Calculate the volume of this cylinder. - Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places. - Dodecagon

Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - Lookout tower

How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now. - Trip with compass

During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip? - A bottle

A bottle full of cola weighs 1,320 g. If we drink three-tenths of it, it will weigh 1,008g. How much does an empty bottle weigh? - Spherical segment

Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.

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