#### Number of problems found: 96

• The cylinder The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder.
• Circle and square An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
• Magnified cube If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm3. Determine the surface of both the original and the magnified cube.
• Birthdays In the classroom, students always give candy to their classmates on their birthdays. The birthday person always gives each one candy, and he does not give himself. A total of 650 candies were distributed in the class per year. How many students are in the
• An equilateral An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?
• Suppose Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
• Uboid volume Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
• Square side If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square? Find the radius of the circle with area S = 200 cm².
• Secret treasure Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
• Three members GP The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
• Isosceles triangle 9 Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle.
• Rectangular garden 2 A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
• Find parameters Find parameters of the circle in the plane - coordinates of center and radius: ?
• 3rd dimension The block has a surface of 42 dm2 and its dimensions are 3 dm and 2 dm. What is the third dimension?
• Completing square Solve the quadratic equation: m2=4m+20 using completing the square method
• Two pipes How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
• Substitution method Solve goniometric equation: sin4 θ - 1/cos2 θ=cos2 θ - 2
• AP RT triangle The length of the sides of a right triangle forms an arithmetic progression, and the longer leg is 24 cm long. What are the perimeter and area?
• Rectangle - area, perimeter The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.

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