Math Examples of Geometric Solids

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area of pyramid = ½ * p * h;
Where, ‘p’ is the perimeter and ‘h’ is the slant height of pyramid.
Given, length = 11 inch;
Slant height = 13 inch;
LSA =?
First we find the perimeter of a pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 11 + 11 + 11;
Perimeter = 33 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
LSA = ½ * 33 * 13;
LSA = ½ * 429;
LSA = 214.5 inch^2;
So LSA of triangular pyramid is 214.5 inch².

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area of pyramid = ½ * p * h;
Where, ‘p’ is the perimeter and ‘h’ is the slant height of a pyramid.
Given, length = 17 inch;
Slant height = 16 inch;
LSA = ?
First we find the perimeter of pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 17 + 17 + 17;
Perimeter = 51 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
LSA = ½ * 51 * 16;
LSA = ½ * 816;
LSA = 408 inch^2;
So LSA of a triangular pyramid is 408 inch².

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area = ½ * p * h;
Given, length = 22 inch;
LSA = 130 inch²;
Slant height =?
First we find the perimeter of a pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 22 + 22 + 22;
Perimeter = 66 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
130 = ½ * 66 * h;
130 = 33 * h;
H = 130 / 66;
H = 1.96 inch;
So height of pyramid is 1.96 inch.

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area of pyramid = ½ * p * h;
Where, ‘p’ is the perimeter and ‘h’ is the slant height of a pyramid.
Given, length = 15.9 inch;
Slant height = 14.5 inch;
LSA =?
First we find the perimeter of a pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 15.9 + 15.9 + 15.9;
Perimeter = 47.7 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
LSA = ½ * 47.7 * 14.5;
LSA = ½ * 691.65;
LSA = 345.82 inch²;
So the LSA of a triangular pyramid is 345.82 inch².

The formula for finding the lateral surface area of a pyramid is given by:
Lateral surface area = ½ * p * h;
Given, length = 25 inch;
LSA = 90 inch²;
Slant height =?
First we find the perimeter of pyramid:
Perimeter of a triangular pyramid is a + b + c;
Perimeter = 25 + 25 + 25;
Perimeter = 75 inch;
On putting these values in the formula we get:
LSA = ½ * p * h;
90 = ½ * 75 * h;
90 = 37.5 * h;
H = 90 / 37.5;
H = 2.4 inch;
So the height of a pyramid is 2.4 inch.

The formula for the Right Circular Cylinder is ⊼r²h.
Given, radius = 11 inch;
Volume = 400 inch³;
Height =?
And the value of ‘⊼’ is 3.14;
Put these values in the formula:
Volume of right circular cylinder = ⊼r²h;
400 = 3.14 * (11²) * H;
400 = 3.14 * 121 * H;
400 = 379.94 * H;
Height = 400 / 379.94 inch.
Height = 1.05 inch;
So the height of a right circular cylinder is 1.05 inch.

The formula for finding the volume of Right Circular Cylinder is ⊼r²h.
Where, ‘r’ is the radius and h is the height of a cylinder.
Given, radius = 10 inch;
Height = 11 inch;
And the value of ‘⊼’ is 3.14;
Volume = ?,
Put these values in the formula:
Volume of right circular cylinder = ⊼r²h;
Volume = 3.14 * (11²) * 10;
Volume = 3.14 * 121 * 10;
Volume = 3.14 * 1210;
Volume = 3799.4 inch³.
So the volume of a right circular cylinder is 3799.4 inch³.

The formula for the Right Circular Cylinder is ⊼r²h.
Given, height = 17 inch;
Volume = 150 inch³;
Radius =?
And value of ‘⊼’ is 3.14;
Put these values in the formula:
Volume of right circular cylinder = ⊼r²h;
150 = 3.14 * r² * 17;
150 = 53.38 * r²;
R² = 150 / 53.38 inch;
R² = 2.81 inch;
R = √ 2.81;
R = 1.67;
So radius of right circular cylinder is 1.67 inch.

The formula for Right Circular Cylinder is ⊼r²h.
Given, radius = 10 inch;
Volume = 250 inch³;
Height = ?
And the value of ‘⊼’ is 3.14;
Put these values in the formula:
Volume of right circular cylinder = ⊼r²h;
250 = 3.14 * (10²) * H;
250 = 3.14 * 100 * H;
250 = 314 * H;
Height = 250 / 314 inch.
Height = 0.79 inch;
So height of right circular cylinder is 0.79 inch.

The formula for finding the volume of Right Circular Cylinder is ⊼r²h.
Where, ‘r’ is the radius and ‘h’ is the height of a cylinder.
Given, radius = 7 inch;
Height = 5 inch;
And the value of ‘⊼’ is 3.14;
Volume =?
On putting these values in given formula:
Volume of right circular cylinder = ⊼r²h;
Volume = 3.14 * (7²) * 5;
Volume = 3.14 * 49 * 5;
Volume = 3.14 * 245;
Volume = 769.3 inch³.
So Volume of Right Circular Cylinder is 769.3 inch³.

Given, radius = 10 inch,
Height = 17 inch,
As we know that the value of π is 3.14,
TSA =?
We know that formula for finding the total surface area of a cylinder is given by:
Total surface area of a cylinder = 2πr (r + h);
Here ‘r’ is the radius of a cylinder,
‘h’ represents the height of a cylinder.
On putting all the values in the given formula we get lateral surface area of cylinder.
So total surface area of a cylinder = 2πr (r + h);
TSA = 2 * 3.14 * 10 (10 + 17);
TSA = 2 * 3.14 * 10 (27);
TSA = 2 * 3.14 * 270;
TSA = 1695.6 inch²,
So the total surface area of a cylinder is 1695.6 inch².

Given, radius = 15 inch,
As we know that the value of ‘π’ is 3.14,
TSA =2000 inch²,
Height =?
We know that the formula for finding the total surface area of a cylinder is given by:
Total surface area of a cylinder = 2πr (r + h);
Here ‘r’ is the radius of a cylinder,
‘h’ represents the height of a cylinder.
On putting all values in the given formula we get lateral surface area of cylinder.
So total surface area of a cylinder = 2πr (r + h);
Or we can write it as:
Total surface area of a cylinder = 2πr² + 2πrh;
2000 = 2 * 3.14 * (15)² + 2 * 3.14 * 15 * h;
2000 = 2 * 3.14 * 225 + 94.2 * h;
2000 = 1413 + 94.2h;
94.2H = 2000 – 1413;
H = 587/94.2;
H = 6.23 inch;
So the height of a cylinder is 8616.16 inch.

Given, radius = 19 inch,
Height = 29 inch,
As we know that the value of π is 3.14,
TSA =?
We know that the formula for finding the total surface area of a cylinder is given by:
Total surface area of a cylinder = 2πr (r + h);
Here ‘r’ is the radius of a cylinder,
‘h’ represents the height of a cylinder.
On putting all the values in the given formula we get lateral surface area of cylinder.
So total surface area of a cylinder = 2πr (r + h);
TSA = 2 * 3.14 * 19 (19 + 29);
TSA = 2 * 3.14 * 19 (48);
TSA = 2 * 3.14 * 912;
TSA = 5727.36 inch²,
So the total surface area of a cylinder is 5727.36 inch².

Given, radius = 15.5 inch,
Height = 19.6 inch,
As we know that the value of ‘π’ is 3.14,
TSA =?
We know that the formula for finding the total surface area of a cylinder is given by:
Total surface area of a cylinder = 2πr (r + h);
Here ‘r’ is the radius of a cylinder,
‘h’ represents the height of a cylinder.
On putting all the values in the given formula we get lateral surface area of cylinder.
So total surface area of a cylinder = 2πr (r + h);
TSA = 2 * 3.14 * 15.5 (15.5 + 19.6);
TSA = 2 * 3.14 * 15.5 (35.1);
TSA = 2 * 3.14 * 544.05;
TSA = 3416.63 inch²,
So the total surface area of a cylinder is 3416.63 inch².

Given, radius = 28 inch,
Height = 21 inch,
As we know that value of ‘π’ is 3.14,
TSA = ?
We know that the formula for finding the total surface area of a cylinder is given by:
Total surface area of a cylinder = 2πr (r + h);
Here ‘r’ is the radius of a cylinder,
‘h’ represents the height of a cylinder.
On putting all the values in the given formula we get lateral surface area of cylinder.
So total surface area of a cylinder = 2πr (r + h);
TSA = 2 * 3.14 * 28 (28 + 21);
TSA = 2 * 3.14 * 28 (49);
TSA = 2 * 3.14 * 1372;
TSA = 8616.16 inch²,
So total surface area of a cylinder is 8616.16 inch².