# Examples for 9th grade - page 25

- Vertical prism

The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism - Forth and back

Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B? - Trapezoid RT

The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumptio - Isosceles trapezoid

The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid. - Horizontal Cylindrical Segment

How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank? - Angles in triangle

The triangle is ratio of the angles α:β = 8:3. Angle γ is 40° greater than α. What are the size of angles of the triangle? - Price of state

Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 1121 (super-gross wage).Then tax him 35.2% employer contribution - Rectangle

The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle. - Two typists

There are two typists who are rewriting the material 705 pages. First can it handle rewrite yourself for 24 days; the second 12 days. First typist wrote material yourself 4 days rest rewrites yourself second typist. How many days will it take rewriting alt - Diameter

If the endpoints of a diameter of a circle are A(10, -5) and B (8, 7), what is the radius of the circle? - Parallelogram

The perimeter of the parallelogram is 202 cm. The length of one side is 1.2-times longer than the length of the shorter side. What is the length of sides of a parallelogram? - Temperature calculus

Calculate percentage of temperature increase if changed from -6 °C to 2 °C? - RT 11

Calculate the area of right tirangle if its perimeter is p = 46 m and one cathethus is 18 m long. - Metal alloy

What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel? - Triangular pyramid

It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm^{3.}What is it content (surface area)? - Sphere

Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere. - Journey

The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane 4 km/h and downhill 5 km/h. From point A to B went 2h 54 min back 3h 6 min. How long is the segment of level pla - Combi-triangle

On each side of the square is marked 2 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square? - Roller

Roller has a diameter of 0.97 m and a width 169 cm. How many m^{2}of road level when he turns 68-times? - Equilateral cylinder

Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 221 cm^{3}. Calculate the surface area of the cylinder.

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