Chapter 7 Mensuration Class 10 Maharashtra Board TextBook Solution
Practice set 7.1 | Q 3 | Page 145
Find the total surface area of a cylinder if the radius of its base is 5 cm and height is 40 cm.
Answer:-
The total surface area of a cylinder can be found by adding the lateral surface area to the area of the two circular bases.
The lateral surface area of a cylinder is the product of the height and the circumference of the base. The circumference of a circle is given by 2πr, where r is the radius of the circle.
So, the lateral surface area of the cylinder is:
Lateral surface area = height x circumference of base Lateral surface area = 40 x 2π(5) Lateral surface area = 400π cm^2
The area of each circular base is πr^2, where r is the radius of the circle.
So, the area of both circular bases is:
Area of circular base = πr^2 Area of circular base = π(5)^2 Area of circular base = 25π cm^2
The total surface area of the cylinder is the sum of the lateral surface area and the area of the two circular bases.
Total surface area = lateral surface area + 2 x area of circular base Total surface area = 400π + 2 x 25π Total surface area = 450π cm^2
Therefore, the total surface area of the cylinder is 450π cm^2.
Using a calculator to approximate π to 3.14, the total surface area of the cylinder is approximately 1413 cm^2.
Solution
The lateral surface area of the cylinder is given by:
$$text{Lateral surface area} = text{height} times text{circumference of base} = 40 times 2pi(5) = 400pi text{ cm}^2$$
The area of each circular base is given by:
$$text{Area of circular base} = pi r^2 = pi(5)^2 = 25pi text{ cm}^2$$
Therefore, the total surface area of the cylinder is given by:
$$text{Total surface area} = text{Lateral surface area} + 2times text{Area of circular base} = 400pi + 2times 25pi = 450pi text{ cm}^2$$
Using a calculator to approximate $pi$ to 3.14, the total surface area of the cylinder is approximately 1413 cm$$^2$$.
Chapter 7 Mensuration Textbook Solution 7.1
Practice set 7.1
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