Question

1. Counting 38 cu. ft. of coal to a ton, how many tons will a coal bin 19 ft long, 6 ft wide and 9 ft
deep contain when level full:
2. A tank open at the top, is made of sheet of iron 1 inch thick. The internal dimensions of the
tank are 4 ft. 8 in. long, 3 ft. 6 in. wide, 4 ft. 4 in. deep. Find a) the weight of the tank when
empty; b) when full of salt water. (salt water weighs 64 lb/ft³, iron is 7.2 times as heavy as
saltwater)
3. The edges of s trunk are 3 ft, 4 ft and 6 ft. A second trunk is twice as long, the other edges are 4 ft by 4 ft. How do their volumes differ?
4. A solid concrete porch consists of three steps and a landing.
The steps have a tread of 11 in., a rise of 7 in., and length
of 7 ft. The landing is 6 ft by 7 ft. How much material was
used in its construction?

Answer 1

Answer on Question #57504 – Math – Geometry

Question

1. Counting 38 cu. ft. of coal to a ton, how many tons will a coal bin 19 ft long, 6 ft wide and 9 ft deep contain when level full?

Solution

The volume of the bin is $V = 19 \cdot 6 \cdot 9 = 1026 \, ft^3$. Then the bin contains $1026 / 38 = 27$ tons.

**Answer:** 27 tons.

Question

2. A tank open at the top, is made of sheet of iron 1 inch thick. The internal dimensions of the tank are 4 ft. 8 in. long, 3 ft. 6 in. wide, 4 ft. 4 in. deep. Find:

a) the weight of the tank when empty;

b) when full of salt water.

(salt water weighs = sw = 64 lb/ft³, iron is 7.2 times as heavy as saltwater).

Solution

Because $1 \, ft = 12 \, in$, length = $l = 4 \, ft$ 8 in = $(4 \cdot 12 + 8) = 56 \, in$; width = $w = (3 \cdot 12 + 6) = 42 \, in$; depth = $d = (4 \cdot 12 + 4) = 52 \, in$;

iron weights = $i = 7.2 \cdot 64 \frac{lb}{ft^3} = 460.8 \frac{lb}{ft^3}$.

The volume of tank is $V_t = 2ld + 2wd + lw + 4d + 2w + 2l + 4 = 2 * 56 * 52 + 2 * 42 * 52 + 56 * 42 + 4 * 52 + 2 * 42 + 2 * 56 + 4 = 12952 \, in^3$.

The weight of the tank when it is empty is $w_T = V_t \cdot i = 12952 \cdot \frac{460.8}{1728} = 3453.8667 \, lb$.

The volume of water is $V_w = l * w * d = 56 * 42 * 52 = 122304 \, in^3$.

The weight of salt water is: $w_{SW} = V_w s_w = 122304 \cdot \frac{64}{1728} = 4529.7778 \, lb$.

The full weight is $W_W = w_T + w_{SW} = 7983.6445 \, lb$.

**Answer:** 3453.8667 lb; 7983.6445 lb.

Question

3. The edges of trunk are 3 ft, 4 ft and 6 ft. A second trunk is twice as long, the other edges are 4 ft by 4 ft. How do their volumes differ?

Solution

The volume of first trunk is $V1 = l_{1} * w_{1} * h_{1} = 3 \cdot 4 \cdot 6 = 72 \, ft^{3}$.

The volume of second trunk is $V_{2} = l_{2} \cdot w_{2} \cdot h_{2} = 6 \cdot 4 \cdot 4 = 96 \, ft^{3}$.

The difference is $V_{2} - V_{1} = 96 - 72 = 24 \, ft^{3}$.

**Answer**: the volume of second trunk is $24 \, ft^{3}$ more than second.

Question

4. A solid concrete porch consists of three steps and a landing. The steps have a tread of 11 in., a rise of 7 in., and length of 7 ft. The landing is 6 ft by 7 ft. How much material was used in its construction?

Solution

The volume of three steps is $V_{p} = 7 \cdot 7 \cdot 11 \cdot (1 + 2 + 3) = 3234 \, in^{3}$.

I don't know the height of landing. Let it be $h$ (unit of measurement – ft), $1 \, ft = 12 \, in$.

Then the volume of landing is $V_{l} = 6 \cdot 7 \cdot h = 42h \, ft^{3} = 42 \cdot 12^{3}h \, in^{3} = 72576h \, in^{3}$.

Total volume is $V = V_{l} + V_{p} = (72576h + 3234) \, in^{3}$.

**Answer**: $(72576h + 3234) \, in^{3}$.

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