Question : If the slant height of a cone is 29 cm and its height is 20 cm, find the ratio between the magnitudes of the total surface area and the volume.
Option 1: 5 : 14
Option 2: 7 : 15
Option 3: 3 : 7
Option 4: 3 : 14
Correct Answer: 5 : 14
Solution : Given, Slant height($l$) = 29 cm Height($h$) = 20 cm ⇒ Radius, $(r) = \sqrt{l^2-h^2}$ ⇒ $r=\sqrt{29^2-20^2}$ ⇒ $r=\sqrt{841-400}$ ⇒ $r=\sqrt{441}$ ⇒ $r=21$ cm Total surface area of cone = $ πr(r + l)$ and volume = $\frac13πr^2h$ $\therefore$ Ratio = $(r+l):(\frac13rh)=(21+29):\frac13\times21\times20=50:140=5 : 14$ Hence, the correct answer is 5 : 14.
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Question : The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm3, then what is the slant height of the cone? (Use $\pi$ = 3.14)
Option 1: 12 cm
Option 2: 11 cm
Option 3: 13 cm
Option 4: 14 cm
Question : The area of the base of a cone is 616 cm2. If its slant height is 20 cm, then what is the total surface area of the cone? [Use $\pi$ = $\frac{22}{7}$]
Option 1: 1352 cm2
Option 2: 1296 cm2
Option 3: 1496 cm2
Option 4: 1524 cm2
Question : The ratio of the total surface area and volume of a sphere is 2 : 7. Its radius is:
Option 1: 7.5 cm
Option 2: 10.5 cm
Option 3: 10 cm
Option 4: 7 cm
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 ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm3, then find its total surface area (take $\pi$ = 3.14).
Option 1: 3391.2 cm2
Option 2: 5391.2 cm2
Option 3: 4391.2 cm2
Option 4: 5591.2 cm2
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