# Right triangle - 9th grade (14y) - math problems

#### Number of problems found: 905

• Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.
• Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
• Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid.
• Body diagonal
Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
• Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
• Total area
Calculate the total area (surface and bases) of a prism whose base is a rhombus which diagonals of 12cm and 18cm and prism height are 10 cm.
• Angle of diagonal
The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
• The cone
The cone with a base radius of 12 cm and a height of 20 cm was truncated at a distance of 6 cm from the base, thus creating a truncated cone. Find the radius of the base of the truncated cone.
• Hexagonal pyramid
Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm.
• Tower
The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?
• Hexagonal prism
The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism.
• The tent
The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
• 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
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
• Glass
How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
• Cube wall
Calculate the cube's diagonal if you know that one wall's surface is equal to 36 centimeters square. Please also calculate its volume.
• Triangular prism
The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the prism's largest wall is 130 cm2, and the body height is 10 cm. Calculate the body volume.
• Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
• The bus stop
The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how much m2 roofing is required to cover the sheathing three walls, taking 40% of the additional coverage.
• Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C', has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.

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