Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

An open-topped glass aquarium with a square base is designed to hold 32 cubic feet of water. What is the minimum possible exterior surface area of the aquarium?
square feet

An open-topped glass aquarium with a square base is designed to hold $32$ cubic feet of water. What is the minimum possible exterior surface area of the aquarium? $\newline$ square feet

View step-by-step help

View step-by-step help

Area and perimeter: word problems

Full solution

Q. An open-topped glass aquarium with a square base is designed to hold

32

cubic feet of water. What is the minimum possible exterior surface area of the aquarium?

\newline

square feet

Define Variables: Let $s$ be the side length of the square base and $h$ be the height of the aquarium. $\newline$ Volume of the aquarium $V = s^2 \times h$ .
Given Volume: Given volume $V = 32$ cubic feet. $\newline$ Substitute $32$ for $V$ in $V = s^2 \cdot h$ . $\newline$ $32 = s^2 \cdot h$ .
Substitute Volume: Since the base is square and we want the minimum surface area, the aquarium will be a cube (where all sides are equal). $\newline$ So, $s = h$ .
Base is a Cube: Substitute $s$ for $h$ in $32 = s^2 \cdot h$ .
$32 = s^2 \cdot s$ .
$32 = s^3$ .
Calculate Side Length: Solve for $s$ . $s = \sqrt[3]{32}$ . $s = 2 \times \sqrt[3]{2}$ .
Calculate Surface Area: Calculate the exterior surface area of the aquarium without the open top. $\newline$ Surface area $A = 4 \times s^2 + s^2$ ( $4$ sides plus the base).
Calculate Surface Area: Calculate the exterior surface area of the aquarium without the open top. $\newline$ Surface area $A = 4 \times s^2 + s^2$ ( $4$ sides plus the base).Substitute $2 \times \text{cube root of } 2$ for $s$ in $A = 4 \times s^2 + s^2$ . $\newline$ $A = 4 \times (2 \times \text{cube root of } 2)^2 + (2 \times \text{cube root of } 2)^2$ . $\newline$ $A = 4 \times 4 \times 2 + 4 \times 2$ . $\newline$ $A = 32 + 8$ . $\newline$ $A = 40$ square feet.

More problems from Area and perimeter: word problems

Question

A rectangular prism with length

\ell

w

h

has a volume of

\ell w h

\newline

What is the volume of a prism which has a base of

5 \mathrm{~m}

3 \mathrm{~m}

, and a height of

4 \mathrm{~m}

\newline

\mathrm{m}^{3}

Posted 10 months ago

Question

Solve for the exact value of

x

\newline

5 \ln (8 x+6)-12=3

\newline

Posted 8 months ago

Question

Solve for the exact value of

x

\newline

2 \ln (2 x-4)+6=16

\newline

Posted 8 months ago

Question

Which measurement is more precise?

\newline

\newline

16

\newline

93.2

Posted 8 months ago

Question

Which measurement is more precise?

\newline

\newline

36.6

\newline

16.51

Posted 8 months ago

Question

Which measurement is more precise?

\newline

\newline

60.72

\newline

19

Posted 8 months ago

Question

Which measurement is more precise?

\newline

\newline

11.45\,\text{cm}

\newline

8.6\,\text{cm}

Posted 8 months ago

Question

Which measurement is more precise?

\newline

\newline

61.8

\newline

39.05

Posted 8 months ago

Question

Which measurement is more precise?

\newline

\newline

21\,\text{km}

\newline

75.18\,\text{km}

Posted 8 months ago

Question

Which measurement is more precise?

\newline

\newline

53.4

\newline

24.33

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant