Question : If the side of an equilateral triangle is 8 cm, then find the area of the triangle (correct to two decimal places).
Option 1: 27.17 cm2
Option 2: 27.27 cm2
Option 3: 27.71 cm2
Option 4: 27.72 cm2
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Correct Answer: 27.71 cm2
Solution : Given: The side of an equilateral triangle = 8 cm So, the area of the equilateral triangle = $\frac{\sqrt3 a^2}{4}$ = $\frac{\sqrt3× 8^2}{4}$ = $16\sqrt3$ = 16 × 1.732 = 27.71 cm2 Hence, the correct answer is 27.71 cm2.
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Question : If the volume of a sphere is 24,416.64 cm3, find its surface area (take $\pi$ = 3.14) correct to two places of decimal.
Option 1: 3069.55 cm2
Option 2: 4069.44 cm2
Option 3: 5096.66 cm2
Option 4: 6069.67 cm2
Question : The external diameter of an iron pipe is 20 cm and its length is 12 cm. If the thickness of the pipe is 1 cm, find the surface area of the pipe (take $\pi=\frac{22}{7}$ ) correct to two places of decimal.
Option 1: 1,662.67 cm2
Option 2: 1,552.57 cm2
Option 3: 1,442.48 cm2
Option 4: 1,772.76 cm2
Question : Let A, B, and C be the mid-points of sides PQ, QR, and PR, respectively, of PQR. If the area of $\triangle$ PQR is 32 cm2, then find the area of $\triangle$ ABC.
Option 1: 24 cm2
Option 2: 16 cm2
Option 3: 32 cm2
Option 4: 8 cm2
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
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
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