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3 years ago

A right prism has height 8 and triangular bases with sides of length 7, 8, and 9. What is the: Total surface area of the prism?

Mathematics

1 answer:

raketka [301]3 years ago

7 0

Answer:

the total surface area of the prism is 245.67

Step-by-step explanation:

Given;

height of the triangular prism, h = 8

length of the triangular bases, = 7, 8, and 9

The total surface area of the prism is calculated as;

T.S.A = ph + 2B

Where;

p is the perimeter of the base

B is area of the base

P = 7 + 8 + 9 = 24

Area of the base can be calculated using Hero's formula;

$S = \frac{7+8+9}{2} = 12\\\\Base \ area (B) = \sqrt{12(12-7)(12-8)(12-9)} = 26.833$

T.S.A = (24 x 8) + 2 x 26.833

T.S.A = 192 + 53.666

T.S.A = 245.67

Therefore, the total surface area of the prism is 245.67

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Calculate the value of (1/2)^4

galben [10]

Answer:

Step-by-step explanation:

(1/2)^4 = 0.063

0.063 as a fraction is 1/16

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3 years ago

A 20 foot ladder is placed against a wall at a 75 degree angle with the ground. The wall is perpendicular to the ground. How hig

Ne4ueva [31]

20 feet

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3 years ago

A roll of 100 pennies is in the shape of a right cylinder. Each penny has a diameter of 0.75 inches and a thickness of 0.04 inch

zalisa [80]

Answer:

(B) π(0.75/2)²(4)

Step-by-step explanation:

The volume formula:

V = πr²h

Given:

d = 0.75 in ⇒ r = d/2 = 0.75/2 in
h = 0.04 in

The volume of each penny:

V = π(0.75/2)²(0.04)

The volume of 100 pennies:

V = 100*π(0.75/2)²(0.04) = π(0.75/2)²(4)

Correct choice is B

6 0

3 years ago

Read 2 more answers

A silo is not the shape of a cone. The silo is 8 meters tall and it's base has a diameter of 3 meters. Soybeans cost $414 per cu

Gnom [1K]

Answer:

$7803.72

Step-by-step explanation:

We have been given that a silo is in the shape of a cone. The silo is 8 meters tall and it's base has a diameter of 3 meters. Soybeans cost $414 per cubic meter. We are asked to find the total cost to fill the silo with soybeans.

First of all, we will find the volume of silo using volume of cone formula.

$\text{Volume of cone}=\frac{1}{3}\pi r^2 h$ , where,

r = radius

h = Height

We know that radius is half the diameter, so radius of silo would be $r=\frac{3}{2}=1.5$ .

$\text{Volume of cone}=\frac{1}{3}\pi (1.5\text{ m})^2 (8)\text{ m}$

$\text{Volume of cone}=\frac{1}{3}\pi\times 2.25\text{ m}^2 (8)\text{ m}$

$\text{Volume of cone}=\pi\times 0.75\text{ m}^2 (8)\text{ m}$

$\text{Volume of cone}=\pi\times 6\text{ m}^3$

$\text{Volume of cone}=18.8495559\text{ m}^3$

Now we will multiply total volume by $414 to find total cost.\

$\text{Total cost of soybeans}=\$414 \times 18.8495559$

$\text{Total cost of soybeans}=\$7803.7161426$

$\text{Total cost of soybeans}\approx \$7803.72$

Therefore, it will cost $7803.72 to fill the silo with soybeans.

5 0

3 years ago

In a doctor's waiting room, there are 14 seats in a row. Eight people are waiting to be seated. Three of the 8 are in one family

lianna [129]

There are 14 chairs and 8 people to be seated. But among the 8. three will be seated together:

So 5 people and (3) could be considered as 6 entities:

Since the order matters, we have to use permutation:

¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆ x 3!

2,162,160 x 6 = 12,972,960 ways.

Another way to solve this problem is as follow:

5 + (3) people are considered (for the time being) as 6 entities:

The 1st has a choice among 14 ways
The 2nd has a choice among 13 ways
The 3rd has a choice among 12 ways
The 4th has a choice among 11 ways
The 5th has a choice among 10 ways
The 6th has a choice among 9ways

So far there are 14x13x12x11x10x9 = 2,162,160 ways
But the 3 (that formed one group) could seat among themselves in 3!
or 6 ways:

Total number of permutation = 2,162,160 x 6 = 12,972,960

4 0

3 years ago