Areas and Volumes of Solids

Write the name of the following prism.

The prism is called a right ____ prims.

How many lateral faces are in the following prism?

What kind of figure in each lateral face in the following prism?

Name two lateral edges and an altitude of the following prism?

The length of an altitude is called the ___ of the following prism.

Consider the following prism.

Suppose the bases are regular hexagons with 4cm 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 prism have equal volumes, must they also have equal total areas?

Find the following.

a.Since 1 yd = 3 ft, 1 yd² = __ ft² and 1 yd³ = __ ft³

b.Since 1 ft = __ in, 1 ft² = __ in² and 1 ft³ = __ in³

c.Since 1 m = __ cm, 1 m² = __ cm² and 1 m³ = __ cm³

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 6\\ w& 4\\ h& 2\\ \text{L.A.}& \\ \text{T.A.}& \\ V& \end{array}$

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 50\\ w& 30\\ h& 15\\ \text{L.A.}& \\ \text{T.A.}& \\ V& \end{array}$

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 6\\ w& 3\\ h& \\ \text{L.A.}& \\ \text{T.A.}& \\ V& 54\end{array}$

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& \\ w& 8\\ h& 5\\ \text{L.A.}& \\ \text{T.A.}& \\ V& 360\end{array}$

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 5x\\ w& 4x\\ h& 3x\\ \text{L.A.}& \\ \text{T.A.}& \\ V& \end{array}$

Refer to rectangular solids with dimensions l, w and h. Complete the following table.

$\begin{array}{cc}l& 9\\ w& \\ h& 2\\ \text{L.A.}& 60\\ \text{T.A.}& \\ V& \end{array}$

Refer to cubes with edges of length e. Complete the following table.

$\begin{array}{cc}e& 3\\ T.A.& \\ V& \end{array}$

Refer to cubes with edges of length e. Complete the following table.

$\begin{array}{cc}e& e\\ T.A.& \\ V& \end{array}$

Refer to cubes with edges of length e. Complete the following table.

$\begin{array}{cc}e& \\ T.A.& \\ V& 1000\end{array}$

Refer to cubes with edges of length e. Complete the following table.

$\begin{array}{cc}e& \\ T.A.& \\ V& 64\end{array}$

Refer to cubes with edges of length e. Complete the following table.

$\begin{array}{cc}e& \\ T.A.& \\ V& 64\end{array}$

$\begin{array}{cc}e& \\ T.A.& \\ V& 64\end{array}$

Refer to cubes with edges of length e. Complete the following table.

$\begin{array}{cc}e& \\ T.A.& 150\\ V& \end{array}$

$\begin{array}{cc}e& \\ T.A.& 150\\ V& \end{array}$

Refer to cubes with edges of length e. Complete the following table.

$\begin{array}{cc}e& 2x\\ T.A.& \\ V& \end{array}$

Find the lateral area of a right pentagonal prism with height 3 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 rectangular solid are all tripled, the lateral area is multiplied by ___, the total area is multiplied by ___, and the volume is multiplied by___.

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

Equilateral triangle with side 8, h = 10.

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

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

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

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

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

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

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

Rhombus with diagonals 6 and 8, h = 9.

Facts about the base of a right prism and the height of the prism are given. Sketch each prism and find its lateral area, total area and volume.

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?

Find the weight to the nearest kilogram, of the cement block shown. Cement weighs 1700 kg/m³?

Find the weight to the nearest 10 kg, of the steel 1- 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.

Accurately draw or construct a large equilateral triangle. Choose any point inside the triangle and carefully measure the distance x, y, z and h. Then find$x+y+z$ .

Now choose another point on or inside the triangle and find$x+y+z$ . What do you notice? Why does this happen?

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 ${35}^{\circ }$ angle with a diagonal of the base. Use trigonometry to approximate the volume of the box.

Suppose another box has a base with dimensions 8 by 6 and diagonal that forms a ${70}^{\circ }$ angle with a diagonal of a base. Show that the ration of the volumes of the two boxes is $\frac{\tan {35}^{\circ }}{\tan {70}^{\circ }}$.

A right prism has height x and bases that are equilateral triangles with sides x. Show that the volume is$\frac{1}{4}{x}^3\sqrt{3}$ .

A right prism has height h and bases that are regular hexagons with sides s. Show that the volume is$\frac{3}{2}{s}^{2}h\sqrt{3}$ .

A rectangular beam of wood 3 m long is cut into 6 pieces. Find the volume of each piece in cubic centimetres.