### Math Exercises & Math Problems: Volume and Surface Area of Solids

Find the volume and surface area of a cube, if the area of its one face is 40 cm^{2}.

Find the volume and surface area of a cube, if you know the length of its space diagonal *d = *216 cm.

Square prism has a base edge *a = *7.1 cm long and a lateral edge *h = *18.2 cm long. Determine its volume and surface area.

Find the volume and surface area of a triangular prism with a right-angled triangle base, if length of the prism base legs are 7.2 cm and 4.7 cm and height of a prism is 24 cm.

Find the volume and surface area of a pillar in a shape of a prism with a rhombus base, which diagonals are *d*_{1 }*= *102 cm, *d*_{2 }*= *64 cm. Height of a pillar is 1.5 m.

Swimming pool with a depth of two meters has the shape of a prism with an isosceles trapezoid bottom. Dimensions of the trapezoid's bases are 10 m and 18 m and legs are 7 m long. During a spring cleaning we have to paint bottom and side walls of the pool. How many m^{2} do we need to paint ?

Cylindrical vase is 28 cm high. Its internal diameter is *d = *1.1 dm. How many liters of water will fill up a vase, if thickness of its bottom is 1.5 cm ?

A cylindrical container with a diameter of 1.8 m contains 2,000 *l* of water. To what height reaches the water ?

Road roller has a diameter of 1.2 m and a width of 180 cm. How many m^{2} of road it will flatten if it turns 35 times ?

What is the weight of 1,000 m of copper wire with a diameter of 5 mm, if density of copper is *ρ* = 8.8 *g*/*cm*^{3} ?

Find the volume and surface area of a square pyramid where the base edge is 45 cm long and the height of the pyramid is 7 cm.

A pyramid has a rectangular base with dimensions of *a = *6 cm, *b = *8 cm. The side edges are all of the same length *s = *12.5 cm. Find the surface area of the pyramid.

A cube with an edge length of 12 dm has inscribed pyramid with the apex at the center of the upper face of the cube. Determine the volume and surface area of the pyramid.

How many liters of air is under the roof of the castle tower, which has a shape of a regular hexagonal pyramid with a base edge length of 3.6 m and a height of 2.5 m, if the supporting pillars occupy about 7% of the space under the roof ?

A cone and a cylinder have the same volume of 180 cm^{3} and the same height of *h = *15 cm. Which of these two solids has a larger surface area ?

Find the volume and surface area of a cone with a base radius *r = *2.3 dm if the height of cone is *h = *46 mm.

We have to paint without base the outside of forty same traffic cones with a base diameter of *d = *36 cm and a height of *h = *46 cm. How many euros we will pay for the color, if we need 500 cm^{3} of a paint color to paint 1 m^{2} and 1 liter of the color costs 8 € ?

Michael modeled from play dough a 15 cm high pyramid with a rectangular base with dimensions of *a = *12 cm and *b = *8 cm. Jane remodeled Michael's pyramid into a cone with a base diameter of *d = *10 cm. What was the height of Jane's cone ?

A kettle 35 cm high has the shape of a truncated pyramid with an edge length of a square bottom base *a = *50 cm and the upper edges of a rectangular base *b*_{1}* = *20 cm and *b*_{2}* = *30 cm. How many liters of water can the kettle hold ?

A gap 2 m deep has the shape of a truncated pyramid with rectangular bases. The length and width of the top base is 3x1.5 m and of the bottom base it is 1x0.5 m. To paint one square meter of a gap surface we need 0.25 liters of a green paint color. How many liters of the paint color we will need, if we want to paint just the side walls and the bottom base of the gap ?

Michelle has two vases in her collection. The first vase has the shape of a cone with the base diameter of *d = *20 cm, the second one has the shape of a truncated cone with the bottom base diameter of *d*_{1}* = *25 cm and the upper base diameter of *d*_{2}* = *15 cm. Which vase can hold more water if the height of both two vases is 0.5 meters ?

20 wooden bowls with a shape of truncated cone have to be painted inside and outside by wood varnish. To paint 200 cm^{2} we need 0.1 liters of varnish. How many liters of varnish do we have to buy, if the bowls are 25 cm high, the bottom of the bowls has a diameter of 20 cm and the upper base has a diameter of 30 cm ?

Gasholder has the shape of a sphere with a diameter of 14 m. How many m^{3} of gas will fit into it ?

What percentage of the volume of a cube with 6 m long edges takes the volume of a sphere inscribed into the cube ?

What percentage of the surface area of a sphere with a radius of 12 cm takes the surface area of a cube inscribed into the sphere ?

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