Question : The total surface area of a square-based right pyramid is 1536 m2, of which 37.5% is the area of the base of the pyramid. What is the volume (in m3) of this pyramid?
Option 1: 3048
Option 2: 3072
Option 3: 3144
Option 4: 3108
Correct Answer: 3072
Solution : Given: Total surface area of pyramid = 1536 m2 Area of base = 37.5% of total surface area = $\frac{37.5}{100}\times1536$ = $\frac{3}{8}\times1536$ = $576$ Remaining area = 1536 – 576 = 960 $\therefore$ lateral surface area = 960 m2 Area of square base = 576 ⇒ $\text{side}^2=576$ $\therefore \text{side}=24$ Perimeter of base = 4 × 24 = 96 We know that, Lateral surface area of pyramid = $\frac{1}{2}$ × perimeter of base × slant height ⇒ $960 = \frac{1}{2} \times 96\times$ slant height $\therefore$ Slant height = 20 $\text{Height} = \sqrt{\text{slant height}^2-(\frac{\text{side}}{2})^2}$ = $\sqrt{20^2-12^2}$ = $16$ Now, Volume of pyramid = $\frac{1}{3}$ × area of base × height = $\frac{1}{3}\times576\times16$ = $3072$ m3 Hence, the correct answer is 3072.
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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 : 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 : The base of the right prism, whose height is 2 cm, is a square. If the total surface area of the prism is 10 cm2, then its volume is:
Option 1: 3 cm3
Option 2: 1 cm3
Option 3: 2 cm3
Option 4: 4 cm3
Question : The ratio of the radius of the base and the height of a solid right circular cylinder is 2 : 3. If its volume is 202.125 cm3, then its total surface area is: (Take $\pi=\frac{22}{7}$)
Option 1: 192.5 cm2
Option 2: 154 cm2
Option 3: 168 cm2
Option 4: 115.5 cm2
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