Area of shape - 8th grade (13y) - examples

1. Ratio of volumes
If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
2. Ratio of sides
Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
3. Iceberg
What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
4. Concentric circles
There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.
6. Pyramid height
Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
7. Garden
Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
8. Right Δ
A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
9. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
10. Triangle SAS
Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
11. Square
Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
12. Rhombus
Calculate the perimeter and area of ​​a rhombus whose diagonals are 38 cm and 55 cm long.
13. Scale
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
14. Regular 5-gon
Calculate area of the regular pentagon with side 7 cm.
15. Tereza
The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
16. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
17. Rectangle
In rectangle with sides, 10 and 8 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
18. Area of RT
Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5.
19. Circles
The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
20. Cylinders
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.