# Worksheet: Surface Areas of Prisms

In this worksheet, we will practice finding the lateral and total surface areas of different types of prisms using more than one formula.

**Q2: **

Suppose the length of each edge of an ice cube is 19 centimeters. The cube is then cut horizontally in half into two smaller rectangular prisms. Determine the surface area of one of the two prisms.

**Q3: **

Mark uses cardboard to build a box 30 cm long, 25 cm wide, and 20 cm high. How much cardboard is needed?

**Q6: **

A regular octagonal prism has base side 17 and height 19. What is its lateral area?

**Q7: **

A student wants to make a net of the rectangular prism shown. Work out the surface area of the net that he would need to draw given that the measurements are in inches.

**Q8: **

Determine the lateral surface area of a cube whose base surface area is 38.44 cm^{2}.

**Q9: **

If the lateral surface area of a cube is 100 cm^{2}, find its volume.

**Q10: **

If the perimeter of one face of a cube is 22.4 cm, determine, to the nearest hundredth, its lateral surface area.

**Q11: **

The lateral surface area of a cube is 576 cm^{2}. What is the perimeter of one of its faces?

**Q15: **

Find, to the nearest tenth, the surface area of a right hexagonal prism if its height is 14 centimeters and each of its base edges is 9 centimeters.

**Q17: **

Given that the volume of a cube is 8 cm^{3}, find its surface area.

**Q18: **

A silver cube has length 18 cm. It is going to be melted and converted into rectangular prisms with dimensions 3 cm, 2 cm, and 12 cm. How many rectangular prisms will this make?

**Q19: **

A silver cube with length 36 cm is melted and poured into a cuboid-shaped mold whose base measures 36 cm by 18 cm. What is the height of the new silver cuboid?

**Q20: **

What is the volume of a cube whose total surface area is 96 m^{2}?

**Q21: **

A rectangular prism has a surface area of 382 square inches, a height of 7 inches, and a width of 5 inches. Determine its volume.

**Q22: **

Two containers are full of mango juice.
The first is a rectangular prism with inner dimensions
of 35 cm,
33 cm, and
35 cm. The second is
a cube with an internal edge length of 30 cm.
All of the juice needs to be poured into bottles
that have a volume of 775 cm^{3}.
How many bottles are required?

**Q23: **

The summed area of two faces of a cube is 60.5. What is its total surface area?

**Q24: **

A factory manufactures closed boxes with 50 cm
sides. How many boxes can be made from 300 m^{2} of cardboard, given that of it is unusable?

**Q25: **

A cubic swimming pool has side 10.5 m. If paint costs 15 LE per square meter, how much does it cost to paint the pool?