Solid geometry, stereometry - page 85 of 123
Number of problems found: 2442
- 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. - Roof material
How many square meters of roofing is needed to cover the cone-shaped roof if the perimeter of its base is 15.7 m and a height of 30 dm - 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. - 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. - Pyramid edge calculation The foundations of a regular truncated quadrilateral pyramid are squares. The lengths of the sides differ by 6 dm. Body height is 7 dm. The body volume is 1813 dm³. Calculate the lengths of the edges of both bases.
- Cone surface volume
Calculate the cone's surface and volume if its base diameter is 1 dm and the side length is 13 cm. - Pool capacity
The pool is 30 m long, 12 m wide, and 2 m deep. Can it contain 7,000 hl of water? If so, what is the level? If not, how much extra water is there? - Ruler case
A cylinder-shaped case is to be made for a ruler with the shape of a prism with a base in the shape of an equilateral triangle with a side length of 3 cm. What must be the smallest inner diameter of the housing? Determine the size to the nearest tenth of - Hexagonal prism 2
The regular hexagonal prism has a surface of 140 cm² and a height of 5 cm. Calculate its volume. - Floating barrel
A barrel (cylindrical in shape) floats on water with its top 18 dm above the water surface. The width of the part of the barrel above the waterline is 34 dm. The length of the barrel is 12 dm. Calculate the volume of the barrel.
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