Question

A concrete tank has an external diameter of 5 m
and an internal height of 3 m. The walls and base
of the tank are 20 cm thick.
a Find the volume of concrete required to make
the base.
b Find the volume of concrete required to make
the walls.
Find the total volume of concrete required.
d Find the cost of the concrete at $142 per m3​

Answer 1

Given:

A concrete tank has an external diameter of 5 m  and an internal height of 3 m.

The walls and base  of the tank are 20 cm thick.

To find:

(a). Find the volume of concrete required to make  the base.

(b). Find the volume of concrete required to make  the walls.

(c). Find the total volume of concrete required.

(d). Find the cost of the concrete at $ 142 per m³​

Solution:

(a). Finding the volume of concrete required to make  the base:

The thickness of the base = 20 cm = 0.20 m

The external diameter of the base = 5 m

∴ The external radius of the base = $\frac{diameter}{2} = \frac{5}{2} = 2.5\: m$

Now,

The volume of the required concrete to make the base is,

= Volume of the cylindrical base

= $\pi r^2h$

= $\frac{22}{7} \times (2.5)^2\times 0.20$

= $\frac{22}{7} \times 6.25\times 0.20$

= $\bold{3.92 \:m^3}$

$\boxed{\bold{Volume \:of\:concrete\:required\:to\:make\:the\:base\:is\:\underline{3.92\:m^3}}}.$

(b). Finding the volume of concrete required to make  the walls:

The external radius, r₂ = 2.5 m

The thickness of the walls = 0.20 m

∴ The internal radius, r₁ = 2.5 - 0.20 = 2.3 m

The internal height = 3 m

Now,

The volume of concrete required to make  the walls of the concrete tank is,

= Volume of the cylindrical walls

= $\pi (r_2^2 - r_1^2)h$

= $\frac{22}{7} \times (2.5^2 - 2.3^2)\times 3$

= $\frac{22}{7} \times (6.25 - 5.29)\times 3$

= $\frac{22}{7} \times 0.96\times 3$

= $\bold{9.05 \:m^3}$

$\boxed{\bold{Volume \:of\:concrete\:required\:to\:make\:the\:walls\:is\:\underline{9.05\:m^3}}}.$

(c). Finding the total volume of the concrete required:

Now,

The total volume of the concrete required is,

= [Volume of concrete required to make the base] + [Volume of concrete required to make the walls]

= 3.92 m³ + 9.05 m³

= 12.97 m³

$\boxed{\bold{The \:total\:volume \:of\:concrete\:required\:to\:make\:the\:tank\:is\:\underline{12.97\:m^3}}}.$

(d). Finding the cost of the concrete:

If the cost of the 1 m ³ of concrete = $142

Then, the cost of 12.97 m³ of concrete = $ 142 × 12.97 m³ = $ 1841.74

$\boxed{\bold{The \:cost\: of\: the\: concrete\: at\: \ \:142 \:per\: m^3\:is\:\underline{\ \:1841.74}}}.$

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