Surface area + Pythagorean theorem - practice problems
Number of problems found: 298
- Cuboid - sum of edges length
Calculate the cuboid's dimensions if the sum of its edges is 19 cm. The body's diagonal size is 13 cm, and its volume is 144 cm³. The total surface area is 192 cm². - A lamp
A lamp shade like that of a frustum has a height of 12 cm and an upper and lower diameter of 10 cm and 20 cm. What area of materials is required to cover the curved surface of the frustum? - A frustum
A frustum of a pyramid consists of a square base of length 10 cm and a top square of length 7 cm. The height of the frustum is 6 cm. Calculate the surface area and volume. - Pentagonal pyramid
Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm.
- Top of the tower
The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m. The pyramid height is 1.6 m. How many square meters of sheet metal are needed to cover the top of the tower if 15% extra sheet metal is needed for join - Pit
The pit is 0.8 m deep and in the shape of a truncated pyramid with a rectangular base. Its length and width are the top 3 × 1.5 m and the bottom 1 m × 0.5 m. To paint one square meter of the pit, we use 0.6 l of green paint. How many liters of paint are n - Traffic cones
Forty identical traffic cones with a base diameter d = 3 dm and height v = 6 dm will be painted orange outside (without the base). If we need 50 cm³ of paint to cover 1 m² and 1 liter of paint costs 80 SKK, how many SKK crowns will we pay? - Iglu - cone tent
The cone-shaped tent is 3 m high, and the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m² of fabric is needed for production (including flooring) if 20% needs to be added to the minimum amount due to cutting waste - The tent
The tent shape of a regular quadrilateral pyramid has a base edge length of a = 2 m and a height of v = 1.8 m. If we have to add 7% of the seams, how many m² of cloth did we need to make the tent? How many m³ of air will be in the tent?
- Four-sided 5917
Mr. Radomír had a misfortune during the last storm; a tree fell on his roof in the shape of a regular four-sided pyramid and destroyed it all. The roof has a base edge length of 8m and a side edge length of 15m. How many m² of roofing will he have to buy? - Church roof 2
The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How much money (CZK) will cost the roof cover sheet if 1 m² of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays, and waste? - Circumference 30781
How many square decimeters of decorative paper are needed to make cone-shaped carnival hats for 46 first-graders if the first-graders head circumference is 49 cm and the cap height is 33 cm? Is it necessary to add 3% paper to the folds? - Canopy
Mr Peter has a metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs to paint the roof with anticorrosion. If the manufacturer specifies the consumption of 1 kg to 3.3 m2, how many kg of color must he buy? - Roof cover
Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m² of sheet metal is needed to cover this roof; if 5.5% of the sheet, we must add for joints and waste.
- Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Big Earth
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km. - Cylinder-shaped 81512
A truncated cone-shaped part with base radii of 4 cm and 22 cm is to be recast into a cylinder-shaped part of the same height as the original part. What base radius will the new part have? - Quadrilateral pyramid
The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place. - Pyramid-shaped roof
A block-shaped shed is covered with a quadrilateral pyramid-shaped roof with a base with sides of 6m and 3m and a height of 2.5m. How many m² (square meters) must be purchased if an extra 40% is calculated for roofing and waste?
The perimeter of the four-sided needle is 48 m, and its height is 2.5 m; how much will the sheet metal for this pyramid cost? If 1m² costs €1.5, a 12% loss due to joints and folds is included in the area.Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
