# Surface area - 9th grade (14y) - examples

- Conical area

A right angled triangle has sides a=11 and b=10 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =? - Three cubes

The body was created by gluing three identical cubes. Its volume is 192 cm^{3.}What is its surface in dm^{2}? - Axial section

Axial section of the cone is equilateral triangle with area 300 m^{2.}Calculate volume of the cone. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2.}Calculate the volume of a cone. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm^{2.} - Sphere

Surface of the sphere is 2260 cm^{2,}weight is 52.2 kg. What is its density? - Gutter

How much metal is needed for production 37 pieces of gutter pipes with the diameter 16 cm and length of 1 m? The plate bends add 7% of the material. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees. - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Cone

Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″. - Cube zoom

How many percent we increase volume and surface of cube, if we magnify its edge by 61%. - Rotation

Right triangle with legs 9 cm and 16 cm rotate around longer leg. Calculate the volume and surface area of the formed cone. - Tower

The top of the tower is a regular hexagonal pyramid with base edge 9.2 meters long and a height 9.6 meters. How many m^{2}of sheet is required to cover the top of the tower if we count 12% of the sheet waste? - Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r_{1}=37 cm, r_{2}=40 cm and its distance v=20 cm. - Prism X

The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 48000 cm^{3.}What is the area of surface of the prism? - Pyramid roof

1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - Cylinder - basics

Cylinder with base radius r = 37 cm and height h=74 cm. Calculate: - Rotary cone

The volume of the rotation of the cone is 104 cm^{3}and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone.

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