Planimetrics - math word problemsStudy plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.
Number of problems found: 2106
- The quadrilateral pyramid
The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
- Rectangle diagonal
The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
- Moivre 2
Find the cube roots of 125(cos 288° + i sin 288°).
- Round skirt
The cut on the round skirt has the shape of an annulus. Determine how much m² of fabric will be consumed on an 80 cm long skirt. The circumference of the waist is a circle with a smaller radius and is 69 cm.
- Density of the concrete
Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg.
- Regular triangular prism
Calculate the surface area of body of regular triangular prism, when the length of its base edge is 6.5 cm and height 0.2 m.
Tailor has an estimated 11 meters of 80 cm wide fabric. He will shape wholly 7 rectangles measuring 80 x 150 cm and nothing fabric does not remain. How many fabric he have?
- Metal tube
Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g.
- Metal rails
Dad needs to improve the edges of the wooden boxes - to be reinforced with metal rails. How many cms of rails will he need if the box has the shape of a prism with the length of the edges 70cm 70cm and 120cm?
- Similarity of squares
The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ?
- The sides
The sides of the rectangle are in a ratio of 3: 5 and its circumference measures 72 cm. Calculate: a) the size of both sides of the rectangle b) the area of the rectangle c) the length of the diagonals
- Outer contact of circles
Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contacts. Calculate the perimeter of the triangle S1S2S3.
- Powerplant chimney
From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
- Regular quadrilateral pyramid
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
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?
How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
- Alcohol from potatoes
In the distillery, 10 hl of alcohol can make from 8 t of potatoes. The rectangular field with dimensions of 600 m and 200 m had a yield of 20 t of potatoes per hectare. How many square meters of area are potatoes grown to obtain one liter of alcohol?
- The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
The plot on which Mr. Kalous is to build a house has the shape of a rectangle. On a 1: 500 scale, its dimensions are 7cm and 5.5cm. Find out the dimensions of the plot. Calculate the parcel size.
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