Examples for 8th grade - page 66
For how many integer values of x can 8, 11 and x be the lengths of the sides of triangle?
If the segment of the line y = -8x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much?
- Trains for people
It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 50 km, with regular train leave at 6:05 and arrive at 7:20, but train is late and has departure at 9:52 and arrive at 11:05.
- Square 2
Points D[9,-1] and B[3,3] are opposed vertices of the square ABCD. Calculate area of the square ABCD.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
- Chord MN
Chord MN of circle has distance from the center circle S 118 cm. Angle MSN is 41°. Determine the radius of the circle.
- Carbon dioxide
Calculate how many grams of oxygen are in 126 g of carbon dioxide CO2. Relative atomic mass of oxygen is 16 and of carbon is 12.
- Extreme temperatures
USA hit extreme heat wave. Calculate percentage of the air temperature change from normal summer temperature 24 °C to 37 °C.
- Widescreen monitor
Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 17 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha
- Cone in cube
The cube is inscribed cone. Determine the ratio of the volume of cone and cube. The ratio express as a decimal number and as percentage.
- Triangle SAA
The triangle has one side long 34 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
Bomber flies 5 km at 1400 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s2.
- Temperature calculus
Calculate percentage of temperature increase if changed from -6 °C to 2 °C?
- Required reserves
Calculate what is the minimum amount of money that bank must hold in cash from your deposit 2100 Eur. How much money is ideally created in the banking system from your deposit if the level of minimum reserve requirement is 2.01%? Consider fractional re
Artificially created island in the shape of a circle with a radius of 50 m is overgrown with grass. The only exception is a landing area for helicopters in the shape of a rectangle measuring 15 m and 8 m. What is the probability that the flying seagull (wi
- Rectangular trapezoid
The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.
Triangle ABC with sides a = 5 cm, b = 3 cm, c = 40mm has a midpoint of K, L, M. How many centimeters is long perimeter of parallelogram KBLM?
- Ice and water
We want to cover rectangular rink with dimensions of 55 m and 25 m with 4cm thick layer of ice. How many liters of water we need if after freezing water increases its volume by 10%?
Daniela and Michael would jointly dug potatoes for 7.5 hours. But if Daniela was working alone she would take 2.5 hours more as if he were working with Michael. Determine how much for the work done by Michael himself and how much Daniela herself.