# Examples for 9th grade

- Adam and Ben

When Ben is so many years old to Adam today, Adam will be 23 years old. When Adam was as old as Ben, Ben was two years old. How old is today Ben and Adam? - Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. - Tree shadow 3

A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ? - Pond

A pond with two open floodgates will emptied in 20 days. A larger floodgate will emptied whole pond in 30 days. For how long would he be emptied with a smaller floodgate. - Water channel

The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow - Inner angles

The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places. - Regular n-gon

In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon. - Photocopier

A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page? - Sequence 11

What is the nth term of this sequence 1,1/2,1/3,1/4,1/5 ? - Arithmetic progression

In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ? - 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 cm^{3.} - Tricolors

From the colors - red, blue, green, black and white, create all possible tricolors. - Krkonose CZ

Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater t - Acres

Two hours 24 students harvested chestnuts on 36 acres. How many square meters harvested one student per hour? - Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3,}a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Mirror

How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m. - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Average speed 4

Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip? - Rectangle 35

Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length. - Roof 7

The roof has the shape of a regular quadrangular pyramid with a base edge of 12 m and a height of 4 m. How many percent is folds and waste if in construction was consumed 181.4m2 of plate?

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