# Examples for 8th grade

- Sphere radius

The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm. - Right triangle trigonometrics

Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - Sales of products

For 80 pieces of two quality products a total sales is 175 Eur. If the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold? - Disc

Circumference of the disk is 78.5 cm. What is the circumference of the circular arc of 32° on the disc? - 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? - Sides od triangle

Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm. - Socks

One pair of socks worth CZK 27. Set of 3 pairs of these socks are sold with 10% discount. How many we will pay CZK for two offered sets of socks? - Storm

So far, a storm has traveled 35 miles in 1/2 hour in direction straight to observer. If it is currently 5:00 p. M. And the storm is 105 miles away from you, at what time will the storm reach you? Explain how you solved the problem. - 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%? - Megapascals

What is the area of crosssection of the piston, if the force of 300 kN produces a pressure of 5 MPa? - Rope

How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)? - Bags

The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights. - Trapezoid

How long are the trapezoid bases with area 24 cm^{2}and height 3 cm. One base is 3 times longer than the shorter. - Family

Mom is 42 years old and her daughters 13 and 19. After how many years will mother as old as her daughter together? - 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. - 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)? - Bicycles

You're the owner of the transport 's learning playground. Buy bicycles of two colors but you've got to spend accurately 120000 Kč. Blue bike costs 3600Kč and red bicycle 3200Kč. - Percentages 5

$5.25 is 7 1/2% of what number? - Trapezoid MO-5-Z8

Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm^{2}. What is the area of the trapezoid KLMN? - Earth and Sun

Earth is 150 million km away from the Sun, 300,000 km of sunlight travels in 1 second. How long will the light come from the Sun to the Earth?

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