# Examples for 8th grade - page 21

- Tiles

The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor. - Rectangle diagonals

It is given rectangle with area 24 cm^{2}a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers. - Family and age ratios

Age of father and son are in the ratio 10:3; age of father and daughter are in the ratio 5:2. How old is father and son, if daughter is 20 years old? In what ratio is age sister and brother? - Distance

Calculate distance between two points X[18; 19] and W[20; 3]. - Quadrant II

Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm. - Bits, bytes

Calculate how many different numbers can be encoded in 16-bit binary word? - Insurance

The owner of the house is insured against natural disasters and pays 0.04% annually of the value of house 77 Eur. Calculate the value of the house. Calculate the probability of disaster, if you know that 48% of the insurance is to pay damages. - Circles

Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square? - Similarity n-gon

9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S_{1}=190 dm^{2}and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm. - Horizon

The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] - Children pool

The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film. - Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 5:3:10. Determine the size of the angles of the triangle ΔABC. - Two workers

Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker? - Cone in cylinder

The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage. - Oil rig

Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes? - Tetrahedral prism

Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm. - Rhombus HP

Calculate area of the rhombus with height 24 dm and perimeter 12 dm. - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - Pizza

A school survey found that 10 out of 11 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza? - Triangular prism

Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.

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