Volume + area - math problems

Number of problems found: 364

• Sphere
Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
• 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)?
• Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface, and diameter of the sphere.
• Cylinder - h2
Cylinder volume is 2.6 liters. Base area is 1.3 dm2. Calculate the height of the cylinder.
• Pit
The pit has the shape of a truncated pyramid with a rectangular base and is 0.8 m deep. The pit's length and width are the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of the pit we use 0.6 l of green color. How many liters of paint are nee
• 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.
• Mystery of stereometrie
Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
• Leveling
Calculate how many 25 kg bags of leveling concrete must be purchased if we leveling room 15 m2 to the "height" 6 mm if consumtion is 1.5 kg per square meter and millimeter thickness.
• Prism X
The prism with the edges of the lengths x cm, 2x cm, and 3x cm has volume 20250 cm3. What is the area of the surface of the prism?
• Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, c has dimensions in the ratio of 9:3:8. If you know that the diagonal wall AC is 86 cm, and the angle between AC and space diagonal AG is 25 degrees.
• Prism
The base of the prism is a rhombus with a side 30 cm and a height 27 cm long. The height of the prism is 180% longer than the side length of the rhombus. Calculate the volume of the prism.
• Pool coating
How many tiles 25 cm × 15 cm need to coat the bottom and sidewalls of the pool with bottom dimensions 30 m × 5 m, if the pool can fit up to 271500 liters of water?
• Center of the cube
The Center of the cube has a distance 16 cm from each vertex. Calculate the volume V and surface area S of the cube.
• Balls
Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
• The pot
The pot is in 1/3 filled with water. Bottom of the pot has an area of ​​329 cm2. How many centimeters rises water level in the pot after add 1.2 liters of water?
• Prism
Calculate the volume of the rhombic prism. The prism base is a rhombus whose one diagonal is 47 cm, and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
• Sawdust
How many cubic centimeters of wood sawdust is created by cut the tree trunk with a diameter of 66 cm and when the gap width is 5 mm?
• Rotary cone
The volume of the rotation of the cone is 472 cm3, and the angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone.
• Cone
Calculate volume and surface area of ​​the cone with a diameter of the base d=15 cm and side of the cone with the base has angle 52°.