# Examples for 8th grade - page 36

- Triangular pyramid

Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm - The hall

The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m^{2.}What were the original dimensions of the hall? - Unknown number

Samuel wrote unknown number. Then he had add 200000 to the number and the result multiply by three. When it calculated he was surprised, because the result would have received anyway, if write digit to the end of original number. Find unknown number. - Rotary cylinder

The rotating cylinder has a surface area 69.08 cm^{2.}The area of the shell is 62.8 cm^{2.}What is the diameter of the cylinder? - Coffee

Coffee from the machine in the cup cost 25 cents. Coffee is 20 cents more expensive than the cup. How much is the cup? - Similarity of squares

The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ? - Aluminum wire

Aluminum wire of 3 mm diameter has a total weight of 1909 kg and a density of 2700 kg/m^{3.}How long is the wire bundle? - BW-BS balls

Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8 What is the ratio of. - Cuboid

The volume of the cuboid is 245 cm^{3.}Each cuboid edge length can be expressed by a integer greater than 1 cm. What is the surface area of the cuboid? - Trough

How many liters of water per second can go via trough, which has a cross section of semicircle with radius 2.5 m and speed of water is 74 cm per second? - Bus stop

Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the - Distance

Wha is the distance between the origin and the point (23; -7)? - Salary

Mr. Johnson's had monthly salary 966 USD since the beginning of year. From which month his salary was increased by 74 USD, when in year earned 11814 USD (enter as a number from 1 to 12)? - Secret number

Determine the secret number n, which reversed decrease by 8.6 if the number increase by 8.6. - Base

Base of building is circle with diameter 39 m. Calculate the circumference of a circular trench witch diameter is 21 cm wider than the diameter of the base. - Tunnels

Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to any - Rectangular triangles

The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c - Glass

Peter broke the window glass with size 110 cm and 90 cm. 1 square meter of glass costs 8 Euro. How much money is need to pay for a new glass? - Equator

Suppose that tourist went on foot over the Globe equator. How many meters more track made his hat on his head as the shoes on your feet? The radius of the earth is 6378 km and height of the tourist is 1.7 m. - Flowerbed

Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 6.1 meters and an angle opposite to the base size is 93°. What is the distance from the base to opposite vertex?

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