Surface area + expression of a variable from the formula - practice problems - page 9 of 19
Number of problems found: 376
- 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. - Tetrahedral prism
Calculate the area and volume of a tetrahedral prism that has a base rhomboid shape, and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm. - Determine 81311
The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm. - Quadrilateral 21523
Calculate the surface area and volume of a regular quadrilateral pyramid if the edge of the lower base is 18 cm and the edge of the upper base is 15 cm. The wall height is 9 cm. - ABCDA'B'C'D 6261
The ABCDA'B'C'D 'prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC 'is 11.4 cm long. Calculate the surface area and volume of the prism. - Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - 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? - Quadrilateral 83324
The volume of a regular quadrilateral pyramid is 72 cm³. Its height is equal to the length of the base edge. Calculate the length of the base and the surface of the pyramid. - Decimeters 83242
The axial section of the cylinder is a square with a content of 56.25 cm². Calculate its surface area and volume. Express the result in square decimeters and cubic decimeters and round to hundredths. - Calculate 74024
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm square. Calculate the radius of the base. - Determine 46401
The volume of the sphere is 20% larger than the volume of the cone. Find its surface if the volume of the cone is 320 cm³. - Cone-shaped 44161
How many square meters of roofing is needed to cover the cone-shaped roof, if the perimeter of its base is 15.7m and a height of 30dm - Calculate 4842
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm. - Calculate 4784
The sketch shows a network of blocks with a surface size of 150 cm². Calculate its volume. (MONITOR 9 - 2005/30 question.) - Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, and height v = 8 cm. - 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. - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Equilateral cylinder
The equilateral cylinder (height = base diameter; h = 2r) has a V = 272 cm³ volume. Calculate the surface area of the cylinder. - Calculate 81034
Calculate the volume of the spherical segment and the surface area of the canopy if the radius of the sphere is r=5cm and the radius of the circular base of the segment ρ=4cm. - Deviation 70434
Frustum has the base radii of the figures r1 and r2: r1> r2, r2 = s, and if the side deviation from the base plane is 60°. Express the surface and volume of the cone frustum using its side s.
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