Volume - math word problems - page 21

1. Scale factor A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
2. Triangular prism Calculate the volume of a triangular prism 10 cm high, the base of which is an equilateral triangle with dimensions a = 5 cm and height va = 4,3 cm
3. Solutions, mixtures How many liters of 70% solution we must add to 5 liters of 30% solution to give us a 60% solution?
4. Five pumps Three same pumps fill the tank with 50400 liters of diesel in 7 hours. How many liters of diesel will it take in 4 hours if we add two more of the same pumps and pump them the same way? How much more (or less) will they get if we add 2 of the same pumps a
5. Ratio of edges The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
6. Angle of diagonal Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume.
7. Stones in aquarium In an aquarium with a length of 2 m, 1.5 m wide and 2.5 m deep, the water is up to three-quarters of the depth. Can we place 2m cubic meters of stones in the aquarium without spilling water? (0 = no, 1 = yes)
8. Volume of cube Solve the volume of a cube with width 26cm .
9. Equilateral cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
10. Find the Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm.
11. Cube, cuboid, and sphere Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
12. Gasoline tank 2 A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters more is needed to fill it? Show your solution.
13. Sand path How many m3 of sand is needed to fill the 1.5m wide path around a rectangular flowerbed of 8m and 14m if the sand layer is 6cm high?
14. Cuboid - Vab Find the surface of the cuboid when its volume is 52.8 cubic centimeters, and the length of its two edges is 2 centimeters and 6 centimeters.
15. Vehicle tank A vehicle tank was 3/5 full of petrol. When 21 liters of fuel was added it was 5/6 full. How many liters of petrol can the tank hold?
16. Square prism Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
17. Three pumps We are filling the pool. The first pump would be filled in 12 hours, the second pump in 15 hours. If all three pumps were running at the same time, it would fill the pool for 4 hours. How long would the pool fill only with the third pump?
18. Volume and body diagonal Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
19. Base of house Calculate the volume of the bases of a square house, if the base depth is 1.2 m, the width is 40 cm and their outer circumference is 40.7 m. Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.