# Examples for 9th grade - page 78

- Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =? - Doubling

The message is spreading that each day has doubled the number of people who know about it. All know message for 20 days. How long known it eighth people? - Cows

Agricultural cooperative has increased the number of housed cows by 14% to 285 units. By how many cows increased agricultural cooperative the number of cows? - 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. - Jane class

When asked how many students are in class, Jane said, if we increase the number of students in our class by hundred % and then add half the number of students, we get 100. How many students are in Jane's class? - Olympics metals

In how many ways can be win six athletes medal positions in the Olympics? Metal color matters. - Diagonals in diamons/rhombus

Rhombus ABCD has side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal. - Regular n-gon

Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm? - Map scale

On a 1:1000 scale map is a rectangular land of 4.2 cm and 5.8 cm. What is the area of this land in square meters? - Content area and percents

Determine what percentage is smaller cube surface, when the surface area of the wall decreases by 25%. - Volleyball

8 girls wants to play volleyball against boys. On the field at one time can be six players per team. How many initial teams of this girls may trainer to choose? - Tree trunk

From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section. - Two sisters

Two sisters together have 54 CDs. 6/8 CDs has younger sister and is equal to 3/5 of CDs older sisters. How many CDs has each of the sisters? - Cube walls

Find the volume and surface area of the cube if the area of one wall is 40cm2. - Boxes

200 boxes have been straightened in three rows. The first was 13 more than in the second, and in the second was one fifth more than in the third one. How many boxes are in each row? - Acid solution

By adding 250 grams of a 96% solution of sulfuric acid to its 3% solution its initial concentration was changed to 25%. How many grams of 3% of the acid were used for dilution? - Triangular prism

The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm^{2}and the body height is 10 cm. Calculate the body volume. - Z9–I–4 MO 2017

Numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of each of the three was equal to the sum of the remaining two. The conducto - Trucks

Three lorries droved bricks. One drove n bricks at once, second m less bricks than the first and third 300 bricks more the first lorry. The first lorry went 4 times a day the largest went 3 times a day and the smallest 5 times a day. How many bricks br - Football season

Dalibor and Adam together scored 97 goals in the season. Adam scored 9 goals more than Dalibor. How many goals scored each?

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