Angle + surface area - practice problems
Number of problems found: 71
- Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - 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'. - Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - 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.
- Conical area
A right-angled triangle has sides a=12 and b=19 at the right angle. The hypotenuse is c. If the triangle rotates on the c side as an axis, find the volume and surface area of the conical area created by this rotation. - Tropics and polar zones
What percentage of the Earth's surface lies in the tropical, temperate, and polar zone? Tropics border individual zones at 23°27' and polar circles at 66°33'. - Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Calculate 3019
The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone. - Pyramid - angle
Calculate the regular quadrangular pyramid's surface whose base edge measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees.
- Cone
Calculate the volume and surface area of the cone with a diameter of the base d=15 cm and the side of the cone with the base has angle 52°. - ----------------- 4850
v = 35 m α = 55 ° β = 15 ° ----------------- X =? Calculate: V- barrack volume =? S- barrack area =? - 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. Find the ratio of surfaces of the first and second bo - Lampshade 7846
Lampshade for the face of a truncated cone with a height of 20 cm. The upper diameter of the shade is 13 cm, the lower 36 cm, and the side forms an angle of 60 degrees with the lower diameter. At least how much fabric is needed to make this shade? - Deviation 4905
The flower bed has the shape of a regular 4-sided pyramid. The edge of the lower plinth is 10 m, and the upper plinth is 9 m. The deviation of the side wall from the base is 45 degrees. How many plantings should be purchased if 90 are needed to plant 1 sq
- A dodecagon
Find the surface area of a regular 12-sided polygon if its side is a = 12 cm. - Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm, and the diagonal body forms a 50-degree angle with the base plane. - Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7, and 8, wherein on different sides are different numbers. John makes the sum of the numbers written on three adjacent walls for each wall. Thus got eight sums, which al - Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =? - Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°.
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