Examples for 8th grade - page 78
- Roof 8
How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
- Type of triangle
How do I find the triangle type if the angle ratio is 2:3:7 ?
- Church roof 2
The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
- Sum of three numbers
The sum of three numbers from which second number is 20% smaller than the first number and the third number is 25% smaller than the second number is 96. Determine this numbers.
Solve the inequation: 5k - (7k - 1)≤ 2/5 . (5-k)-2
The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
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.
- Regular octagon
Draw the regular octagon ABCDEFGH inscribed with the circle k (S; r = 2.5 cm). Select point S' so that |SS'| = 4.5 cm. Draw S (S '): ABCDEFGH - A'B'C'D'E'F'G'H'.
In the Hockey World Cup play eight teams, determine how many ways can they win gold, silver and bronze medals.
John, Teresa, Daniel and Paul have summary 56 years. Their ages are in a ratio of 1:2:5:6. Determine how many years have each of them.
- Outer angles
The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C?
- Circle r,D
Calculate the diameter and radius of the circle if it has length 63.69 cm.
- Copper parts
From copper cast were made 3 parts. At first consumed one third of casting, the second 2/3 of rest and the third weighed 18 kg. What is the weight of original copper cast?
Drivers of passenger cars have calculated that at a speed of 60 km/h arrives at destination within 40 minutes. After 20 km refrain five minutes due a technical failure. How fast must go the rest of the way to the finish came at the scheduled time?
- Mason with assistant
Mason had to complete the work in 10 days. Two and a half days later his assistant arrived. Together they completed the work in next three and a half days. How many days would he need an assistant for the same work?
- Four friends
Four friends shared the money. Vasek got 1/4 of the total amount. Tonda received 1/3 of the rest of the money, Joe got a half from the second residue and Jirka left 80. How much money get together?
- Brick wall
Garden 70 m long and 48 m wide should surround with wall 2.1 meters high and 30 cm thick. How many we will need bricks if to 1 m³ is needed approximately 300 bricks?
- Reciprocal equation
Determine the root of the equation: 9/x-7/x=1
- Fit ball
What is the size of the surface of Gymball (FIT - ball) with a diameter of 65 cm?
- Alcohol mixture
From 55% and 80% alcohol we have to produce 0.2 kg of 60% alcohol. How many of them do we use in solution?