Area - 9th grade (14y) - math problems
- Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
- Triangular prism
Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm.
- Two hemispheres
In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)?
A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
- The bases
The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
- Annulus from triangle
Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
- Rectangular land
On a rectangular land with dimensions of 35 m and 18.5 m is a house with a square floor plan with a side of 14 m. What % of the land is not occupied?
- Compute 4
Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
- Two gardens
The total area of the two gardens is 864 m2. The first garden is 60 m2 smaller than three times the second garden. What is the area of each garden?
- Storm and roof
The roof on the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m2 of roof need to be repaired if 20% were damaged in a storm?
One bag of urea containing 46 percent nitrogen weighs 25 kg. How many bags have to be purchased for fertilizing a field of 41003 square meters if the nitrogen dose is 50.0 kg per hectare?
- Rectangular base pyramid
Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters.
- Triangular prism
Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm.
- Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
- Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco
- The Indian tent
The Indian tent is cone-shaped. Its height is 3.5 m. The diameter of the base is 2.5 m. How much canvas is needed to make a tire?
- Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.
- The trapezium
The trapezium is formed by cutting the top of the right-angled isosceles triangle. The base of the trapezium is 10 cm and the top is 5 cm. Find the area of trapezium.
- Folding table
The folding kitchen table has a rectangular shape with an area of 168dm2 (side and is 14 dm long). If necessary, it can be enlarged by sliding two semi-circular plates (at sides b). How much percent will the table area increase? The result round to one-hu