# Examples for 9th grade - page 59

- Diagonal - simple

Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm. - Coins

In ticket maschine were together one hundred coins. They were only 20 and 50 cent coins. The sum total was 29 euros and 60 cents. How many were in ticket maschine coins and which type? - Cuboid - edges

The sum of all edges cuboid are 11 meters. However, the width is twice shorter than the length and height is seven times longer than the width. Determine the dimensions of the cuboid. - Force meter

We put the statuette on the force meter. The force meter showed a value 25 N. Then we placed the statuette on the force meter completely immersed in the water. The force meter showed a value 17 N. What is the volume of the statuette? - Enrollment

The enrollment at a local college increased 3% over last year's enrollment of 7145. Find the increase in enrollment (x_{1}) and the current enrollment (x_{2}). - Triangle

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 177 b = 124 c = 63 - Task of the year

Determine the number of integers from 1 to 10^{6}with ending four digits 2001. - Cube

Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm^{2.} - Cuboid walls

Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm². - Concrete block

Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters. - Combined interest

Combined interest: Carol has deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. The money was put into the account 5.5.2016 and withdraw them all before Christmas 20.12.2016. How much money did she withdraw? - Cone area and side

Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side. - Rectangle

Perimeter of rectangle is 48 cm. Calculate its dimensions if they are in the ratio 5:3 (width:height) - 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? - Truncated cone

A truncated cone has a base radius 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume. - Prism

Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m. - Average mark

Calculate average mark in English, if a student got a couple of 3's, 20% less 2 than 3, and 50% more 1's than the 2's. - Tree shadow

The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)? - Pyramid 4sides

Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm. - Two masons

Two masons built the garage together - it took 18 days. If they worked independently, the other would work 15 days more than the first. For how many days would build the garage each mason himhelp?

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