Chapter 6

Find the lateral area, total area, and volume of each of the following right circular cylinders: (a) Base diameter \(=34.5\) in., height \(=26.4\) in. (b) Base diameter \(=134 \mathrm{cm},\) height \(=226 \mathrm{cm}\) (c) Base diameter \(=3.65 \mathrm{cm},\) height \(=2.76 \mathrm{m}\)

Find the circumference and area of a circle of radius \(4.82 \mathrm{cm} .\)

An oblique prism has a base area of 5.63 in. \(^{2}\) and an altitude of 4.72 in. Find its volume.

Find the area and perimeter of (a) a square of side 5.83 in. (b) a square of side \(4.82 \mathrm{m}\) (c) a rectangle measuring \(384 \mathrm{cm} \times 734 \mathrm{cm}\) (d) a rectangle measuring 55.4 in. by 73.5 in.

Find the volume and the lateral area of a right circular cylinder having a base radius of 128 and a height of 285.

Find the circumference and area of a circle of radius 2.385 in.

The base of a right prism is an equilateral triangle 3.74 mm on a side. Its altitude is \(8.35 \mathrm{mm}\). Find its volume and lateral area.

Find the area of (a) a parallelogram whose base is \(4.52 \mathrm{ft}\) and whose altitude is \(2.95 \mathrm{ft}\). (b) a parallelogram whose base is \(16.3 \mathrm{m}\) and whose altitude is \(22.6 \mathrm{m}\) (c) a rhombus whose base is \(14.2 \mathrm{cm}\) and whose altitude is \(11.6 \mathrm{cm}\) (d) a rhombus whose base is 382 in. and whose altitude is 268 in. (e) a trapezoid whose bases are \(3.83 \mathrm{m}\) and \(2.44 \mathrm{m}\) and whose altitude is \(1.86 \mathrm{m}\) (f) a trapezoid whose bases are \(33.6 \mathrm{ft}\) and \(24.7 \mathrm{ft}\) and whose altitude is \(15.3 \mathrm{ft}\).

Find the radius and area for a circle whose circumference is 74.8 in.

What will be the cost, to the nearest dollar, of flagging a sidewalk 312 ft long and \(6.5 \mathrm{ft}\) wide, at \(\$ 13.50\) per square yard?

Find the radius and area for a circle whose circumference is \(2.73 \mathrm{m}\)

How many 9 -in.-square tiles will cover a floor 48 ft by 12 ft?

A certain steel bushing is in the shape of a hollow cylinder \(18.0 \mathrm{mm}\) in diameter and \(25.0 \mathrm{mm}\) long, with an axial hole \(12.0 \mathrm{mm}\) in diameter. Find the volume of steel in one bushing.

Find the radius and circumference of a circle whose area is \(39.5 \mathrm{ft}^{2}\).

Find the radius and circumference of a circle whose area is \(2.74 \mathrm{m}^{2}\).

A certain gasoline engine has four cylinders, each with a bore of \(82.0 \mathrm{mm}\) and a piston stroke of \(95.0 \mathrm{mm}\). Find the engine displacement in liters. (The engine displacement is the total volume swept out by all of the pistons.)

The radius of a circle is \(5.00 \mathrm{m} .\) Find the diameter of another circle containing 4 times the area of the first.

Find the lateral area and the volume enclosed by a cylindrical tower having a round base \(18.0 \mathrm{ft}\) in diameter and a height of \(31.5 \mathrm{ft}\).

What will it cost to cement the floor of a cellar \(25.3 \mathrm{ft}\) long and \(18.4 \mathrm{ft}\) wide, at \(\$ 3.50\) per square foot?

A cylindrical chimney has a round base with a 2.55 m outside diameter, a 2.00 m inside diameter, and a height of 7.54 m. Find the volume of masonry in the chimney.

Find the surface area and volume of a cube with the following sides: a. 3.75 in. b. \(26.3 \mathrm{cm}\) c. \(2.24 \mathrm{ft}\)

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. What is the cost, to the nearest dollar, of a triangular piece of land whose base is \(828 \mathrm{ft}\) and altitude is \(412 \mathrm{ft}\) at \(\$ 1125\) an acre? \(\left(1 \text { acre }=43,560 \mathrm{ft}^{2}\right).\)

A circular hole for a wading pool, \(3.00 \mathrm{ft}\) deep and \(32.0 \mathrm{ft}\) in diameter, is to be dug in level ground. How many cubic yards of earth must be removed?

Find the volume and surface area of a rectangular parallelepiped that measures \(26.8 \mathrm{cm} \times 83.4 \mathrm{cm} \times 55.3 \mathrm{cm}\).

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. A vertical pole \(45.0 \mathrm{ft}\) high stands on level ground and is supported by three guy wires attached to the top and reaching the ground at distances of \(60.0 \mathrm{ft}, 108.0 \mathrm{ft},\) and \(200.0 \mathrm{ft}\) from the foot of the pole. What are the lengths of the wires?

A cylindrical oil tank is \(4.50 \mathrm{ft}\) in diameter and \(7.20 \mathrm{ft}\) long. Find its capacity, in gallons. \(\left(1 \mathrm{ft}^{3}=7.48 \text { gal }\right)\)

A 1.00 -in. cube of steel is placed in a surface grinding machine, and the vertical feed is set so that 0.0050 in. of metal is removed from the top of the cube at each cut. How many cuts are needed to reduce the volume of the cube by 0.50 in. \(^{3} ?\)

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. A ladder 39.0 ft long reaches to the top of a building when its foot stands \(15.0 \mathrm{ft}\) from the building. How high is the building?

In a park is a circular fountain whose basin is \(22.5 \mathrm{m}\) in circumference. What is the diameter of the basin?

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. Two streets, one \(16.2 \mathrm{m}\) and the other \(31.5 \mathrm{m}\) wide, cross at right angles. What is the diagonal distance between the opposite corners?

The area of the bottom of a circular pan is 196 in. \(^{2} .\) What is its diameter?

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. A rectangular room is \(20.0 \mathrm{ft}\) long. \(16.0 \mathrm{ft}\) wide, and \(12.0 \mathrm{ft}\) high. What is the diagonal distance from one of the lower corners to the opposite upper corner?

Miter Angles: Calculate the miter angle \(\theta\) for a (a) triangular window (equilateral) (b) square or rectangular frame (c) hexagonal window (d) octagonal wall clock

Find the diameter of a circular solar pond that has an area of \(125 \mathrm{m}^{2}\).

The circumference of the base of a right circular cone is 40.0 in., and the slant height is 38.0 in. What is the area of the lateral surface?

Board Feet. A board foot of lumber is the volume of wood contained in a board 1 in. thick, 1 ft long, and 1 ft wide. How many cubic inches and cubic feet are in a board foot?

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. What is the side of a square whose diagonal is \(50.0 \mathrm{m} ?\)

What is the circumference of a circular lake \(33.0 \mathrm{m}\) in diameter?

Find the volume of a circular cone whose altitude is \(24.0 \mathrm{cm}\) and whose base diameter is \(30.0 \mathrm{cm}\).

Board Feet. How many board feet are in a plank that is \(2^{1} / 2\) in. thick, 15 in. wide, and 18 ft long?

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. A rectangular park \(125 \mathrm{m}\) long and \(233 \mathrm{m}\) wide has a straight walk running through it from opposite corners. What is the length of the walk?

Board Feet. How many board feet are contained by 12 two-by-fours, cach 8 ft long? (Board feet calculations normally use the rough or unplaned dimensions, so here use the nominal \(2 \times 4\) dimensions rather than the actual ones).

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. A ladder \(32.0 \mathrm{ft}\) long stands flat against the side of a building. How many feet must it be drawn out at the bottom so that the top may be lowered \(4.00 \mathrm{ft} ?\)

A woodcutter uses a tape measure and finds the circumference of a tree to be 95.0 in. Assuming the tree cross-section to be circular, what length of chainsaw bar is needed to fell the tree? (By cutting from both sides, one can fell a tree whose diameter is twice the length of the chain-saw bar.)

Estimate the volume of a conical pile of sand that is \(12.5 \mathrm{ft}\) high and has a base diameter of \(14.2 \mathrm{ft}\).

Volume of Excavations. How many cubic yards of earth must be removed for a rectangular cellar hole dug on level ground, 48 ft long, 36 ft wide, and 12 ft deep?

To help you solve each problem, draw a diagram and label it completely. Look for special triangles or right triangles contained in the diagram. Be sure to look up any word that is unfamiliar. The slant height of a cone (Fig. \(6-42\) ) is 21.8 in., and the diameter of the base is 18.4 in. How high is the cone?

What must be the diameter \(d\) of a cylindrical piston so that a pressure of \(125 \mathrm{lb} / \mathrm{in.}^{2}\) on its circular end will result in a total force of \(3610 \mathrm{lb} ?\) Hint: The \(\mathrm{f}\) a surface is equal to the area of that surface times the pressure on that surface.

Find the volume of a tapered steel roller \(12.0 \mathrm{ft}\) long and having end diameters of 12.0 in. and 15.0 in.

Conds of Firewood. A standard cord of wood is a " well-stacked" pile measuring \(4 \mathrm{ft}\) by \(4 \mathrm{ft}\) by \(8 \mathrm{ft}\). How many cubic feet of wood are in a cord?