# Examples for 7th grade (seventh)

1. Two rectangles I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm2. What dimensions can this large rectangle have? Write all options. Explain your calc
2. Glass with icecream We have 6 kinds of ice cream and 5 kinds of fruit. We put 3 cups of ice cream and 2 fruits into each glass. How many can unique decorated glasses be?
3. Regular prism The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
4. Sand path How many m3 of sand is needed to fill the 1.5m wide path around a rectangular flowerbed of 8m and 14m if the sand layer is 6cm high?
5. Cube edges The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.
6. The diagram The diagram is a cone of radius 8cm and height 10cm. The diameter of the base is. ..
7. Two angles The triangles ABC and A'B'C 'are similar. In the ABC triangle, the two angles are 25° and 65°. Explain why in the triangle A'B'C 'is the sum of two angles of 90 degrees.
8. Simplify 2 Simplify expression: 5ab-7+3ba-9
9. Curved surface area CSA A cylinder 5cm high has a base radius(7/2) cm. Calculate the curved surface area.
10. Bus vs train Milada took the bus and the journey took 55 minutes. Jarmila was 1h 20 min by train. They arrived in Prague at the same time 10h45 min. At what time did each have to go out?
11. If one If one litre of pant covers an area of 5 m2 how much paint is needed to cover: a) rectangular swimming pool With dimensions 4m x 3m x 2.5m (the Inside walls and the floor only) b) the Inside walls and floor of a cylindrical reservoir with diameter 3m an
12. Triangular prism Calculate the surface of a regular triangular prism with a bottom edge 8 of a length of 5 meters and an appropriate height of 60 meters and prism height is 1 whole 4 meters.
13. Customary length Convert length 65yd 2 ft to ft
14. The volume The volume of a solid cylinder is 260 cm3 the cylinder is melt down into a cuboid, whose base is a square of 5cm, calculate the height of the cuboid and the surface area of the cuboid
15. Three friends Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
16. Triangular prism Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
17. Barrels Peter has 42 barrels. One-sixth of them are filled with lemonade, one third is filled with wine and half is empty. Calculate how many barrels are with each filling. If we read the book at a speed of 15 pages a day, we read it 3 days before we read it at a speed of 10 pages per day. If I read at 6 pages per day, how many days will I read the book? Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm. The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank?