Question : The total surface area of a regular triangular pyramid with each edge of length 1 cm is:
Option 1: $4 \sqrt{3}$ cm2
Option 2: $\frac{4}{3} \sqrt{3}$ cm2
Option 3: $\sqrt{3}$ cm2
Option 4: $4$ cm2
Correct Answer: $\sqrt{3}$ cm2
Solution : A regular triangular pyramid, also known as a tetrahedron, has four equilateral triangles as its faces. The surface area of an equilateral triangle $ = \frac{\sqrt{3}}{4} a^2$ Since a regular tetrahedron has four faces. The total surface area is four times the surface area of one face $=4 \times \frac{\sqrt{3}}{4} a^2 = \sqrt{3} a^2$ Putting \(a = 1 \, \text{cm}\), The total surface area of a regular triangular pyramid $= \sqrt{3}$ cm2 Hence, the correct answer is $ \sqrt{3}$ cm2.
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Question : The total surface area of a right circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)
Option 1: 4312 cm3
Option 2: 3696 cm3
Option 3: 4002 cm3
Option 4: 4851 cm3
Question : A right square pyramid having a lateral surface area is 624 cm2. If the length of the diagonal of the square is $24 \sqrt{2}$, then the volume of the pyramid is:
Option 1: 1150 cm3
Option 2: 780 cm3
Option 3: 1083 cm3
Option 4: 960 cm3
Question : The total surface area of a right pyramid on a square base of side 10 cm with height 12 cm is:
Option 1: 260 cm2
Option 2: 360 cm2
Option 3: 330 cm2
Option 4: 300 cm2
Question : What is the difference between the total surface area and the curved surface area of a cone whose radius is 35 cm? (Take $\pi=\frac{22}{7}$)
Option 1: 3850 cm2
Option 2: 3704 cm2
Option 3: 3750 cm2
Option 4: 3675 cm2
Question : A hemisphere has a 42 cm diameter. Find its curved surface area and the total surface area.
Option 1: 2772 cm2 and 4158 cm2
Option 2: 3772 cm2 and 5158 cm2
Option 3: 4770 cm2 and 4238 cm2
Option 4: 3072 cm2 and 4058 cm2
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