A water company has two storage tanks shaped like right cylinders.

Tank A has a diameter of 30 meters and a height of 10 meters.
Tank B has a diameter of 35 meters and a height of 8 meters.
To the nearest cubic meter, how much greater is the volume of Tank B than the volume of Tank A?

To find how much greater the volume of Tank B is compared to Tank A, we need to calculate the volume of both tanks and then find the difference.

The volume \( V \) of a right circular cylinder is given by the formula:

\[
V = \pi r^2 h
\]

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14159.

### Volume of Tank A
- Diameter = 30 meters, so radius \( r_A = \frac{30}{2} = 15 \) meters.
- Height \( h_A = 10 \) meters.

The volume of Tank A is:

\[
V_A = \pi r_A^2 h_A = \pi (15)^2 (10) = \pi (225) (10) = 2250\pi \, \text{cubic meters}
\]

Approximating \( \pi \):

\[
V_A \approx 2250 \times 3.14159 = 7068.58 \, \text{cubic meters}
\]

### Volume of Tank B
- Diameter = 35 meters, so radius \( r_B = \frac{35}{2} = 17.5 \) meters.
- Height \( h_B = 8 \) meters.

The volume of Tank B is:

\[
V_B = \pi r_B^2 h_B = \pi (17.5)^2 (8) = \pi (306.25) (8) = 2450\pi \, \text{cubic meters}
\]

Approximating \( \pi \):

\[
V_B \approx 2450 \times 3.14159 = 7696.40 \, \text{cubic meters}
\]

### Difference in Volume
The difference in volume between Tank B and Tank A is:

\[
\text{Difference} = V_B - V_A = 7696.40 - 7068.58 = 627.82 \, \text{cubic meters}
\]

Rounding to the nearest cubic meter:

\[
\text{Difference} \approx 628 \, \text{cubic meters}
\]

Thus, the volume of Tank B is approximately **628 cubic meters greater** than the volume of Tank A.

Would you like further details on any part of the solution?

Here are 5 related questions for practice:
1. How would the volumes change if the height of Tank A was doubled?
2. What would the volume difference be if Tank B's diameter was increased to 40 meters?
3. How do changes in the height of a cylinder affect its volume compared to changes in its radius?
4. Can you calculate the surface area of Tank A and Tank B?
5. What is the volume difference between two tanks if Tank A’s radius was reduced by 2 meters?

**Tip:** For cylinders, small changes in radius have a bigger impact on volume than changes in height because the radius is squared in the volume formula!

A water company has two storage tanks shaped like right cylinders. Tank A has a diameter of 30 meters and a height of 10 meters. Tank B has a diameter of 35 meters and a height of 8 meters. To the nearest cubic meter, how much greater is the volume of Tank B than the volume of Tank A?

This problem explores the volume comparison between two cylindrical water storage tanks, Tank A with a diameter of 30 meters and a height of 10 meters, and Tank B with a diameter of 35 meters and a height of 8 meters. Learn how to calculate the difference in volumes using the formula V = πr^2h. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation