Question : The base of a right prism is an equilateral triangle whose side is 10 cm. If the height of this prism is $10 \sqrt{3}$ cm, then what is the total surface area of the prism?
Option 1: $125 \sqrt{3}$ cm2
Option 2: $325 \sqrt{3}$ cm2
Option 3: $150 \sqrt{3}$ cm2
Option 4: $350 \sqrt{3}$ cm2
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Correct Answer: $350 \sqrt{3}$ cm2
Solution :
Given: The base of a right prism is an equilateral triangle whose side is 10 cm. The height of this prism is $10 \sqrt{3}$ cm. The total surface area of the prism = [2(area of triangular base)] + [3(Area of rectangular sides)] The area of an equilateral triangle = $\frac{\sqrt3}{4}\times{\text{side}^2}$ The area of a rectangle = length × breadth The area of an equilateral triangle $=\frac{\sqrt3}{4}\times{{10}^2}=25\sqrt3$ cm2 The area of a rectangle $=10\times 10\sqrt3=100\sqrt3 $ cm2 The total surface area of the prism $=2\times 25\sqrt3+3\times 100\sqrt3$ $=50\sqrt3+300\sqrt3=350 \sqrt{3}$ cm2 Hence, the correct answer is $350 \sqrt{3}$ cm2.
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Question : The height of an equilateral triangle is $7 \sqrt{3}$ cm. What is the area of this equilateral triangle?
Option 1: $36 \sqrt{3}$ cm2
Option 2: $25 \sqrt{3}$ cm2
Option 3: $49 \sqrt{3}$ cm2
Option 4: $32 \sqrt{3}$ cm2
Question : The base of a solid right prism of height 10 cm is a square and its volume is 160 cm3. What is the total surface area of the prism (in cm2)?
Option 1: 200
Option 2: 176
Option 3: 192
Option 4: 180
Question : The base of a prism is a right-angled triangle with two sides 5 cm and 12 cm. The height of the prism is 10 cm. The total surface area of the prism is:
Option 1: 360 sq cm
Option 2: 300 sq cm
Option 3: 330 sq cm
Option 4: 325 sq cm
Question : A prism has a regular hexagonal base with a side of 6 cm. If the total surface area of the prism is 216$\sqrt3$ cm2, then what is the height (in cm) of the prism?
Option 1: $3\sqrt3$
Option 2: $6\sqrt3$
Option 3: $6$
Option 4: $3$
Question : A pyramid has an equilateral triangle as its base, of which each side is 8 cm. Its slant edge is 24 cm. The whole surface area of the pyramid (in cm2) is:
Option 1: $(16 \sqrt{3}+24 \sqrt{35})$
Option 2: $(12 \sqrt{3}+24 \sqrt{35})$
Option 3: $(24\sqrt{3}+36\sqrt{35})$
Option 4: $(16\sqrt{3}+48\sqrt{35})$
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