# Right triangle + surface area - practice problems

#### Number of problems found: 252

- The roof

The tower's roof has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long, and the side wall of the animal with the base at an angle of 57°. Calculate how much roofing we need to cover the entire roof if we count on 15% waste. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, c has dimensions in the ratio of 9:3:8. If you know that the diagonal wall AC is 86 cm, and the angle between AC and space diagonal AG is 25 degrees. - 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. - Triangular prism

The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism. - 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'. - Right triangular prism

We have a cuboid with a base and dimensions of 12 cm and 5 cm and a height of 4 cm. The tablecloth is cut into two identical triangular prisms with right triangular bases. We painted the surface of the created prisms with color. Calculate the surface area - 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. - Rotary bodies

The rotating cone and the rotary cylinder have the same volume of 180 cm³ and the same height v = 15 cm. Which of these two bodies has a larger surface area? - 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 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Church roof

The roof of the church tower has the shape of a regular tetrahedral pyramid with a base edge length of 5.4 meters and a height of 5 m. It was found that the 27% covering of the roof area needs to be corrected. What amount of material will be required? - Martians

A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal? - Ratio-cuboid

The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid. - Cone container

The Rotary cone-shaped container has a volume of 1000 cubic cm and a height of 12 cm. Calculate how much metal we need for making this package. - Prism

The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters? - Tropics and polar zones

What percentage of the Earth's surface lies in the tropical, temperate, and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'. - Calculate 5789

Calculate the volume and surface of the rotating cone with the base radius r = 4.6dm and the height v = 230mm. - Pyramid in cube

In a cube with an edge 12 dm long, we have an inscribed pyramid with the apex at the center of the cube's upper wall. Calculate the volume and surface area of the pyramid. - Triangular pyramid

Calculate a regular triangular pyramid's volume and surface area with a height equal to the base edge 10 cm long. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}, and the angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone.

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