Fractions + expression of a variable from formula - math problems

Cube in a sphere
The cube is inscribed in a sphere with volume 3234 cm³. Determine the length of the edges of a cube.
Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm². Calculate the volume of a cone.
Cone
Circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
Garden
Father dig up the garden in 9 hours. Son in 13 hours. How many hours take dig up the garden together?
Pumps
Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
BMI index
Calculate BMI (body mass index, an index indicating obesity, overweight, normal weight, underweight) man weighing m = 71 kg and height h = 170 cm. Index is calculated according to equation (formula): ? With BMI index is possible to compare people of diff
Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
Direct route
From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t
Trapezoid thirds
The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
Average speed
When the bus stops at bus stops driving average speed is 45 km/h. If it did not stop it drive at speed 54 km/h. How many minutes of every hour it spend at stops?
Unknown number 5
Daniel think an integer. When he change this number at a ratio of 2:5 he got number 2.8. Determine what number think Daniel.
Family
Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?
Orchard
3/5 of the trees in the orchard are apples, 1/3 are cherries and the remaining five trees are pear. How many trees are in the orchard?
Red balls
In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%?
Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
Boys and girls
There are 28 girls in the hall. 5/7 of all children are boys. How many children and how many boys are there?
Right triangle from axes
A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 sq. Units . The segment passes through the point ( 5,2). What is the slope of the line segment. ?
Simple equation 3
24 = n • 27, solve for n
Two friends
Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and then replaced by Martin. Whole work was done in 6.5 hours. Calculate how long Peter worked before replaced by Martin.
The tank
The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank?