A diagonal of a box forms a 35 angle with a diagonal of the base, asshown. Use

The prism is called a right L_ prism.

How many lateral faces are there?

What kind of figure is each lateral face?

Name two lateral edges and an altitude

The length of an altitude is called the __2 . of the prism.

Suppose the bases are regular hexagons with 4 cm edges. a. Find the lateral area. b. Find the base area. c. Find the total area. d. Find the volume.

Can a prism have lateral faces that are triangles?

What is the minimum number of faces a prism can have?

If two prisms have equal volumes, must they also have equal total areas?

a. Since 1 yd = 3 ft, 1 yd2 = _^ ft 2 and 1 yd3 = ^_ ft 3 . b. Since 1 ft = c. Since 1 m = in., 1 ft 2 cm, 1 m2 in." and 1 ft . cm2 and 1 nv in. cm

Exercises 7-12 refer to cubes with edges of length e. Complete the table.

Exercises 7-12 refer to cubes with edges of length e. Complete the table.

Find the lateral area of a right pentagonal prism with height 13 and base edges 3.2, 5.8, 6.9, 4.7, and 9.4.

A right triangular prism has lateral area 120 cm2 . If the base edges are 4 cm, 5 cm, and 6 cm long, find the height of the prism.

If the edge of a cube is doubled, the total area is multiplied by :_ and the volume is multiplied by ?

If the length, width, and height of a rectangular solid are all tripled, the lateral area is multiplied by __L_, the total area is multiplied by :_, and the volume is multiplied by ?

Equilateral triangle with side 8; h = 10

Triangle with sides 9, 12, 15; h = 10

Isosceles triangle with sides 13, 13, 10; h = 7

Isosceles trapezoid with bases 10 and 4 and legs 5; h = 20

Rhombus with diagonals 6 and 8; h = 9

Regular hexagon with side 8; h = 12

The container shown has the shape of a rectangular solid. When a rock is submerged, the water level rises 0.5 cm. Find the volume of the rock.

A driveway 30 m long and 5 m wide is to be paved with blacktop 3 cm thick. How much will the blacktop cost if it is sold at the price of $175 per cubic meter?

A brick with dimensions 20 cm, 10 cm, and 5 cm weighs 1.2 kg. A second brick of the same material has dimensions 25 cm. 15 cm. and 4 cm. What is its weight?

A drinking trough for horses is a right trapezoidal prism with dimensions shown below. If it is filled with water, about how much will the water weigh? {Hint: 1 m3 of water weighs 1 metric ton.)

Find the weight, to the nearest kilogram, of the cement block shown. Cement weighs 1700 kg/nr

Find the weight, to the nearest 10 kg. of the steel I-beam shown below. Steel weighs 7860 kg/m3 .

Find the volume and the total surface area of each solid in terms of the given variables.

Find the volume and the total surface area of each solid in terms of the given variables.

The length of a rectangular solid is twice the width, and the height is three times the width. If the volume is 162 cm3 , find the total area of the solid.

A right prism has square bases with edges that are three times as long as the lateral edges. The prism's total area is 750 m2 . Find the volume.

A diagonal of a box forms a 35 angle with a diagonal of the base, as shown. Use trigonometry to approximate the volume of the box.

Refer to Exercise 33. Suppose another box has a base with dimensions 8 by 6 and a diagonal that forms a 70 angle with a diagonal of a base. Show that the ratio of the volumes of the two boxes is tan 35 tan 70'

A right prism has height x and bases that are equilateral triangles with sides x. Show that the volume is \xi \j2>.

A right prism has height h and bases that are regular hexagons with sides 5. Show that the volume is f s 2 hy/3.

A rectangular beam of wood 3 m long is cut into six pieces, as shown. Find the volume of each piece in cubic centimeters.

A rectangular beam of wood 3 m long is cut into six pieces, as shown. Find the volume of each piece in cubic centimeters. A diagonal of a cube joins two vertices not in the same face. If the diagonals are 4\/3 cm long, what is the volume?

All nine edges of a right triangular prism are congruent. Find the length of these edges if the volume is 54 V3cm3

If the length and width of a rectangular solid are each decreased by 20%, by what percent must the height be increased for the volume to remain unchanged? Give your answer to the nearest whole percent.