Question

volume of a cylinder sheet 2
use the measurements to find the volume of these cylinders. give your answers to 2 decimal places.
1)
2)
3)
4)
5)

Explanation:

Problem 1: Cylinder with radius 15 cm and height 7 cm

Step 1: Recall the formula for the volume of a cylinder

The volume \( V \) of a cylinder is given by the formula \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step 2: Substitute the given values into the formula

Here, \( r = 15 \) cm and \( h = 7 \) cm. So we have:
\( V = \pi \times (15)^2 \times 7 \)

Step 3: Calculate the value

First, calculate \( 15^2 = 225 \). Then multiply by 7: \( 225 \times 7 = 1575 \). Now multiply by \( \pi \) (using \( \pi \approx 3.14159 \)):
\( V \approx 3.14159 \times 1575 \approx 4948.00 \) (rounded to 2 decimal places)

Step 1: Recall the volume formula \( V=\pi r^2h \)

Step 2: Substitute \( r = 4.5 \) in and \( h=\frac{16}{3} \) in

\( V=\pi\times(4.5)^2\times\frac{16}{3} \)

Step 3: Calculate the value

First, \( 4.5^2 = 20.25 \). Then \( 20.25\times\frac{16}{3}= 20.25\times\frac{16}{3}= 108 \). Now multiply by \( \pi\approx3.14159 \):
\( V\approx3.14159\times 108\approx 339.29 \) (rounded to 2 decimal places)

Step 1: Use the volume formula \( V = \pi r^2h \)

Step 2: Substitute \( r = 1.2 \) m and \( h = 6.3 \) m

\( V=\pi\times(1.2)^2\times 6.3 \)

Step 3: Calculate the value

First, \( 1.2^2=1.44 \). Then \( 1.44\times 6.3 = 9.072 \). Now multiply by \( \pi\approx3.14159 \):
\( V\approx3.14159\times 9.072\approx 28.49 \) (rounded to 2 decimal places)

Answer:

Working Out: \( V = \pi \times 15^2 \times 7 \approx 4948.00 \) \( \text{cm}^3 \)
Volume: \( 4948.00 \) \( \text{cm}^3 \)

Problem 2: Cylinder with diameter 9 in (so radius \( r=\frac{9}{2}=4.5 \) in) and height \( h = 5\frac{1}{3}=\frac{16}{3} \) in