Solid geometry, stereometry - page 85 of 123

Number of problems found: 2441

Calculate cylinder
A cylinder has a volume V = 120 cm³ and a height v = 4 cm. Calculate the radius and the lateral surface area S.
Cube in a sphere
A cube is inscribed in a sphere with volume 8101 cm³. Determine the edge length of the cube.
Cuboid
A cuboid with edge a = 6 cm and space diagonal u = 31 cm has a volume of V = 900 cm³. Calculate the lengths of the other two edges.
Suitcase - rod
The boot of a car has the shape of a cuboid with dimensions 1.6 m × 1.2 m × 0.5 m (width × depth × height). Determine the longest thin rod that can be placed flat on the bottom of the boot.
The diameter 4
The cone's diameter is 14 ft, and the height is 7 ft. What is the slant height?
Hexagon, hexa S, V
What is the surface area and volume of a regular hexagonal prism with a base edge of 12 cm and a height equal to the diameter of the circle circumscribed about the base?
4B - truncated pyramid
Calculate the volume of a regular truncated quadrilateral pyramid if the base edges are 10 cm and 4 cm and the slant height of the lateral face is 5 cm.
Box
A paper box is in the shape of a cube. 2,400 cm² of paper was used to make it (not including folds for gluing the walls). Calculate the volume of the box.
Cylinder axial section
The axial section of the cylinder is a square with an area of 56.25 cm². Calculate its surface area and volume. Express the result in square decimeters and cubic decimeters and round to hundredths.
The perimeter
The perimeter of the base of a regular quadrilateral pyramid is the same as its height. The pyramid has a volume of 288 dm³. Calculate its surface area round the result to the whole dm².
The radius
A right circular cone's radius and slant heights are 9 cm and 15 cm, respectively. Find, correct to one decimal place, the (i) Height (ii) Volume of the cone
Axial section
The diagonal of the axial section of the rotating cylinder is 6 cm, and its surface is 30 cm². Calculate the radius of the base.
Quadrilateral pyramid
A quadrilateral pyramid has a rectangular base with 24 cm and 13 cm dimensions. The height of the pyramid is 18 cm. Calculate: 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid
Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube.
Pyramid surface volume
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.
A concrete pedestal
A concrete pedestal has the shape of a right circular cone and a height of 2.5 feet. The diameters of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the pedestal's lateral surface area, total surface area, and volume.
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?
Tent
Calculate how many liters of air will fit in the tent with a shield in the shape of an isosceles right triangle with legs r = 3 m long, the height = 1.5 m, and a side length d = 5 m.
Box volume
Calculate the volume of a wooden box in the shape of a prism with the base of a rectangle if the box's width is 8 dm, the length is 14 dm, and the size of the body diagonal is 25 dm.
Equilateral cylinder
The equilateral cylinder (height = base diameter; h = 2r) has a V = 178 cm³ volume. Calculate the surface area of the cylinder.

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