# Unit conversion - 7th grade (12y) - math problems

- The water tank

The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m^{2}? - AL wire

What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram. - Central angle

What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°? - Water tank

300hl of water was filled into the tank 12 m long and 6 m wide. How high does it reach? - A map

A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field? - Chestnuts

Three divisions of nature protectors participated in the collection of chestnut trees.1. the division harvested 1250 kg, the 2nd division by a fifth more than the 1st division and the 3rd division by a sixth more than the second division. How many tons of - Garden exchange

The garden has the shape of a rectangular trapezoid, the bases of which have dimensions of 60 m and 30 m and a vertical arm of 40 m. The owner exchanged this garden for a parallelogram, the area of which is 7/9 of the area of a trapezoidal garden. What is - Winch drum

Originally an empty winch drum with a diameter of 20 cm and a width of 30 cm on the rescue car, he started winding a rope with a thickness of 1 cm beautifully from edge to edge. The winch stopped after 80 turns. It remains to spin 3.54m of rope (without h - Oak trunk

Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³. - Cone from cube

The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m^{3} - Rain

Garden shape of a rectangle measuring 15 m and 20 m rained water up to 3 mm. How many liters of water rained on the garden? - A swiming

A swiming pool holds 30000lt of water. How many gallons does it hold? 1 gallon= 4.55lt - Two rectangular boxes

Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface. - Surface of the cube

Find the surface of the cube that has volume 1/1m3 2/0.001 m^{3}3/8000 mm^{3} - Lunch

Lunch is given to seniors from 12:15 to 12:40 during the Coronavirus pandemic. What angle will the minute hand of clock describe during this time? - Marlon

Marlon drew a scale drawing of a summer camp. In real life, the sand volleyball court is 8 meters wide. It is 4 centimeters wide in the drawing. What is the drawing's scale factor? Simplify your answer and write it as a ratio, using a colon. - Half-filled

A cylindrical pot with a diameter of 24 cm is half-filled with water. How many centimeters will the level rise if we add a liter of water to it? - Average speed

The average speed of a pedestrian who walked 10 km was 5km/h, the average speed of a cyclist on the same track was 20km/h. In how many minutes did the route take more than a cyclist? Q - Calculate

Calculate the surface of a regular quadrilateral prism whose base edge is 2.4dm and the height of the prism is 38cm. - The prison ball

Calculate the density of the material that the prison ball is made from if you know its diameter is 15cm and its weight is approximately 2.3kg. With the help of mathematical-physicochemical tables estimate what material the ball is made from.

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