Question

exercise 14e.2
1 calculate the volume of:
a
b
c
d
e
f

Explanation:

Part a:

Step1: Recall the volume formula for a prism (Volume = Base Area × Length)

The base area is \(1.73 \, m^2\) and the length is \(3.2 \, m\).

Step2: Calculate the volume

\(Volume = 1.73 \times 3.2 = 5.536 \, m^3\)

Part b:

Step1: Recall the volume formula for a prism (Volume = Base Area × Height)

The base area is \(74.6 \, cm^2\) and the height is \(5 \, cm\).

Step2: Calculate the volume

\(Volume = 74.6 \times 5 = 373 \, cm^3\)

Part c:

Step1: Recall the volume formula for a prism (Volume = Base Area × Length)

The base area is \(33.6 \, cm^2\) and the length is \(11.6 \, cm\).

Step2: Calculate the volume

\(Volume = 33.6 \times 11.6 = 389.76 \, cm^3\)

Part d:

Step1: Recall the volume formula for a pyramid (Volume = \(\frac{1}{3}\) × Base Area × Height)

The base area is \(142.3 \, cm^2\) and the height is \(24.9 \, cm\).

Step2: Calculate the volume

\(Volume = \frac{1}{3} \times 142.3 \times 24.9 = \frac{142.3 \times 24.9}{3} = \frac{3543.27}{3} = 1181.09 \, cm^3\)

Part e:

Step1: Recall the volume formula for a cone (Volume = \(\frac{1}{3}\) × Base Area × Height)

The base area is \(14.2 \, cm^2\) and the height is \(7.8 \, cm\).

Step2: Calculate the volume

\(Volume = \frac{1}{3} \times 14.2 \times 7.8 = \frac{14.2 \times 7.8}{3} = \frac{110.76}{3} = 36.92 \, cm^3\)

Part f:

Step1: Recall the volume formula for a cone (Volume = \(\frac{1}{3}\) × Base Area × Height)

The base area is \(4.2 \, m^2\) and the height is \(1.87 \, m\).

Step2: Calculate the volume

\(Volume = \frac{1}{3} \times 4.2 \times 1.87 = \frac{4.2 \times 1.87}{3} = \frac{7.854}{3} = 2.618 \, m^3\)

Answer:

a) \(5.536 \, m^3\)
b) \(373 \, cm^3\)
c) \(389.76 \, cm^3\)
d) \(1181.09 \, cm^3\)
e) \(36.92 \, cm^3\)
f) \(2.618 \, m^3\)