Examples for 9th grade - page 56
- Surface area
The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
- Chord 3
What is the radius of the circle where the chord is 2/3 of the radius from the center and has a length of 10 cm?
- The hall
The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
- Rectangular trapezoid
The rectangular trapezoid having bases length 3.2 cm and 62 mm. The shorter arm has a length 0.25 dm. Calculate the lengths of the diagonals and the second arm.
A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance?
- Iron fence
One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3.
- Chemical parison
The blown parison (with shape of a sphere) have a volume 1.3 liters. What is its surface?
- The city
In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?
- The farmer
The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 54, 71 and 44 meters. Find a suitable way to determine the.
- Cardboard box
We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal
- Repair company
The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 6 residue cars. How many total cars company repaired?
- Percentage of waste
In a square plate with side 42 cm we cut 4 same circles. Calculate the percentage of waste.
- The chord
Calculate a chord length which the distance from the center of the circle (S, 20 cm) equals 7 cm.
- Train from Brno
First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.
- Three men
Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
- Trapezoid - diagonal
Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
- Garden pond
Concrete garden pond has bottom shape of a semicircle with a diameter 1.1 m and is 47 cm deep. Daddy wants make it surface. How many liters of water is in pond if watel level is 22 cm?
- Tourist Jirka
Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
- Quadratic function
It is given a quadratic function y = -5x2+12x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.
- Mystery of stereometrie
Two regular tetrahedrons have surfaces 48 cm2 and 108 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.