Examples for 8th grade - page 69
- Lamp cone
Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
- Octagonal mat
Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat?
- Perimeter of circle
Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
- Volume of three cuboids
Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm.
- Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
The length of segment AB is 24 cm and the point M and N divided it into thirds. Calculate the circumference and area of this shape.
- Math heart
Stylized heart shape created from a square with side 5 cm and two semicircles over his sides. Calculate the content area and its circumference.
- Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
- Circle r,D
Calculate the diameter and radius of the circle if it has length 63.69 cm.
- Two trains meet
From A started at 7:15 express train at speed 85 km/h to B. From B started passenger train at 8:30 in the direction to A and at speed 55 km/h. The distance A and B is 386 1/4 km. At what time and at what distance from B the two trains meet?
Truck take you the some amount of clay in 30 hours. Second truck in 40 hours. Trucks carted the clay away some time together then the second truck broke down and the first one completed the job in five hours. What time worked together?
- Bus stop
Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
- Three monks
Three medieval monks has task to copy 600 pages of the Bible. One rewrites in three days 1 page, second in 2 days 3 pages and a third in 4 days 2 sides. Calculate for how many days and what day the monks will have copied whole Bible when they begin Wednesd
- Four ropes
TV transmitter is anchored at a height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used in the construction of the transmitter. At each attachment.
The thickness of a metallic tube is 1cm and its outer radius is 11cm. Find the mass of such 1m long tube, if the density of the metal is 7.5g per cubic cm.
The width of the rectangle is 65% of its length. Perimeter of the rectangle is 132 cm. Determine the dimensions of the rectangle.
Repairman has vowed to do repair work at the plant for 25 days. However work had to be shortened, and therefore he took helper worker. Together they made all the corrections for the whole days. How long it would take work to helper worker?
- Hiker and cyclist
At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker?
- Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.