Examples for 9th grade - page 49
- Round table
Round table with diameter d = 95 cm is coated by square tablecloth with a side length 122 cm. About how many cm is higher center of tablecloth than its cornes?
- Axial section
Axial section of the cylinder has a diagonal 15 cm long and we know that the area of the side and the area of base is in ratio 1:1. Calculate the height and radius of the cylinder base.
- Slope of the pool
Calculate slope (rise:run) of the bottom of swimming pool long 40 m. Water depth at beginning of pool is 1.15 m (for children) and depth at end is 1.92 m (for swimmers). Slope express as percentage and as angle in degrees.
- Two runners
Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute
- Rectangles - sides
One side of the rectangle is 25 cm longer than second. Shortens longer side by 14 cm and extend shorter by 13 cm increases the area of the rectangle by 130 cm2. What are the dimensions of the original rectangle?
- Similarity coefficient
The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of the larger triangle.
Calculate the volume of a cuboid ABCDEFGH if |AB| = 11 cm, |BC| = 8 cm and the angle ∠CDG = 29.4°
- SAS triangle
The triangle has two sides long 7 and 19 and included angle 144°11'59″. Calculate area of this triangle.
Calculate the circumference and area of the rhomboid with sides 11 and 17, with their angle 70°.
Calculate perimeter of the circle described by a triangle with sides 418, 59, 430.
What is the distance (length) the Earth's meridian 27° when the radius of the Earth is 6370 km?
- Sphere cuts
At what distance from the center intersects sphere with radius R = 60 plane, if the cut area and area of the main sphere circle is in ratio 3/6.
- Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 236 dm.
- Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel.
- Angles in triangle
The triangle is ratio of the angles α:β = 8:3. Angle γ is 40° greater than α. What are the size of angles of the triangle?
- Profitable bank deposit 2012
Calculate the value of what money lose creditor with a deposit € 7700 for 4 years if the entire duration are interest 2.2% p.a. and tax on interest is 19% and annual inflation is 3.6% (Calculate what you will lose if you leave money lying idle at negative
- Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
- Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei
If the current way to school was 2 km shorter then if Milan swipe one half he will have already one quarter of the way to school behind. How long is Milan's way to school?
- Diagonals of a rhombus
One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.