# Examples for 8th grade

#### Number of problems found: 2907

- Cube surface area

The surface of the cube was originally 216 centimeters square. The surface of the cube has shrunk from 216 to 54 centimeters sq. Calculate how much percent the edge of the cube has decreased. - Inlet and outlet

The pool has a capacity of 50 hl. The inlet pipe flows in 1 minute 1.25 hl, and the waste pipe outlet is draining the full pool in 50 minutes. How long will take the empty the full pool when both the inlet and outlet are opened at the same time? - Salt

Sea water containing 5% salt. How many kg of fresh water necessary to pour into 40 kg of sea water so that the salinity fell to 2%? - Exchange rates

If the Canadian dollar appreciated by C$0.005 relative to the US dollar, what would be the new value of the Canadian dollar per US dollar? Assume the current exchange rate was US$1 = C$0.907. - Cube 1-2-3

Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm. - The string

They cut 113 cm from the string and divided the rest in a ratio of 5: 6.5: 8: 9.5. The longest part measured 38 cm. Find the original length of the string. - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Regular quadrangular pyramid

The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes? - Ratio of sides

Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7. - Cone and the ratio

Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface. - Book reading

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? - Square - increased perimeter

How many times is increased perimeter of the square, where its sides increases by 150%? If the perimeter of square will increase twice, how much% increases the content area of the square? - Similarity

ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity. - Draw a trapezoid

Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task. - Regular quadrilateral pyramid

Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. - The base 2

The base diameter of a right cone is 16cm and it's slant height is 12cm. A. ) Find the perpendicular height of the cone to 1 decimal place. B. ) Find the volume of the cone, convert to 3 significant figure. Take pie =3.14 - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square, and the side length is 13 cm. - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Prism

The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters? - River

From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river.

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