Examples for the calculation of the surface area of the solid object
- 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
- Axial section of the cone
The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
- Cone side
Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
- Length of the edge
Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
- 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?
- Surface area of a cube
What is the surface area of a cube that has an edge of 3.5?
The 1.8m cylinder contains 2000 liters of water. What area (in dm2) of this container is the water?
- Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
- A concrete pedestal
A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
- Surface of the cylinder
Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm
- The plaster cast
The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area.
- Gutter pipe
How many m² of sheet metal is required to produce a 12 m long and 18 cm wide gutter, if 7% bend is required?
- Tetrahedral pyramid
A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
- The cylinder 2
Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
- Space diagonal
The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
- Base of prism
The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
How much m² of fabric do we need to sew a 50cm-shaped cube-shaped seat if 10% of the material we add to the folds?
- Water depth
How many square meters of the inside of the pool wet the water if the pool is 25 meters long and 10 meters wide and the water depth is 1.2 meters everywhere.
- Sphere VS
Find the surface and volume of a sphere that has a radius of 2 dm.