Surface Area and Volume of Geometrical Shapes

State the three-dimensional shape that has geometrical characteristics as stated below.

• One circular base.

• One apex.

• One curved surface that merges the base and the apex.

(a)  

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

The diagram shows a sphere with the radius, r = 14 cm. Calculate the surface area of the sphere ( use pi = 22/7)

• 2464 m²

• 1342 cm²

• 2464 cm²

• 2314 cm²

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

The diagram shows a cone. The circle is 4 cm. Calculate the surface area of the cone. Use (pi = 22/7)

• 75.43 cm²

• 122.10 cm²

• 65.34 cm²

• 113.14 cm²

This diagram shows an object made up of a pyramid and a cube. Calculate the surface area of the object. State your answer in cm² .

• 46 m²

• 46 000 cm²

• 32 000 cm²

• 66 000 m²

Calculate the volume of the combined shapes.

• 213.11 m³

• 142 m³

• 155.22 m³

• 118.55 m³

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Calculate the surface area of this geometrical shapes.

• 400 m²

• 320 m²

• 144 m³

• 644 m²

Tags

CCSS.7.G.B.6

A cylinder open at the top with a height twice the radius of the base, is filled with water three quarter full. 539 ml water is needed to fill up the cylinder. Calculate the surface area of the cylinder. in cm². ( Use pi = 3.143)

• 770 cm²

• 1221 cm²

• 772 cm²

• 812 cm²

The diagram shows a bolck of cone and pyramid. If the volume of the pyramid is three times the volume of the cone, and the surface area of the pyramid is twice the surface of the cone, calculate the height of the cone and the pyramid, if the height of the cone is 18 cm.

(Use pi = 3.143)

• 123 cm

• 33 cm

• 22 cm

• 45 cm

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Ali poured water into a cylindrical container that has a radius of 7 cm and height of 15 cm until it is full. A solid shaped cone is inserted fully into the cylinder. After a while, the solid cone is taken out from the cylinder. Calculate the volume of the water that is left in the cylinder.

• 2221.44 cm³

• 2192.67 cm³

• 1934.22 cm³

• 957 cm³

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

A block of metal pyramid with a square base, with side 15 cm and height 10 cm is melted down to form a few balls of sphere with a radius of 5 mm. How many pyramid blocks are needed to form 2850 ball of spheres?

• 2

• 5

• 7

• 4

Tags

CCSS.HSG.GMD.A.3