Examples for 9th grade - page 71
- Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
- Rabbits 3
Viju has 40 chickens and rabbits. If in all there are 90 legs. How many rabbits are there with Viju?
- Pyramid Z8–I–6
Each brick of pyramid contains one number. Whenever possible, the number in each brick is lowest common multiple of two numbers of bricks lying directly above it. That number may be in the lowest brick? Determine all possibilities.
Trader ordered from the manufacturer 200 cut glass. The manufacturer confirmed the order that the glass in boxes sent a kit containing either four or six glasses. Total sent 41 boxes. a) How many boxes will contain only 4 glasses? b) How many boxes will co
- Cuboid edges in ratio
Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
- 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'.
Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
- Timber log
The ship goes from point x to y. Downstream it takes 4 hours, upstream 6 hours. How long does it take from a point x to y a log?
- Three numbers
What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)?
- Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
- 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.
- Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
- 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?
- Roses 2
Aunt Rose went to the flower shop to buy a bouquet with three roses. The flower shop had white, yellow and red roses. How many different flowers bouquet can a flower make for Aunt Rose create? Write all the bouquet options.
- Chord circle
The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
- Two numbers
We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
- Divisible by 5
How many three-digit odd numbers divisible by 5, which are in place ten's number 3?
- 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?
How many three-digit natural numbers do not have the number 7?