# 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 - Leg

Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg. - Rhombus diagonal

Area of rhombus is 224. One diagonal measures 33, find length of other diagonal. - Series

Andrew wrote this series of numbers: 1,3,7,15, .... n. Which number in the series does not belong? ? - Circle arc

Calculate the area of the circular arc in m^{2}where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places. - Snowman 2

On the medal, which has the shape of a circle with a diameter 18 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles express - Chord AB

What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm? - Diagonals in the diamond

The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m^{2.}Determine the sizes of the diagonals. - Loan

Apply for a $ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity. - Pedestrian

Pedestrian came started at 8h in the morning with speed 4.4 km/h. At half-past eleven cyclist started at 26 km/h same way. How many minutes take cyclist to catch up pedestrian? - Common chord

Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles? - Chemical parison

The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface? - 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? - 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)? - Line

Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p? - Baker

The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough? - Exp

If ?, then n is: - Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei - Subway

Subway train went between two stations that gradually accelerated for 26 seconds and reached a speed of 72 km/h. At this rate, went 56 seconds. Then 16 seconds slowed to a stop. What was the distance between the stations? - Earth's diameter

The Earth's diameter on the equator is approximately 12750 km. How long does the Gripen flyover the Earth above the equator at 10 km if it is at an average speed of 1500 km / h?

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