Question:
If the frustum of a cone has radii \(18\) cm and \(6\) cm on either of its ends and its slant height is \(13\) cm, then the volume (in cu. cm) of that frustum is
If the frustum of a cone has radii \(18\) cm and \(6\) cm on either of its ends and its slant height is \(13\) cm, then the volume (in cu. cm) of that frustum is
Show Hint
For frustum problems, if slant height is given, use Pythagoras theorem to find the vertical height first.
Updated On: Jul 15, 2026
- \(720\pi\)
- \(740\pi\)
- \(780\pi\)
- \(820\pi\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
Volume of frustum:
\[
V=\frac13\pi h(R^2+r^2+Rr)
\]
where:
\[
R=18,\; r=6
\]
First find the height using slant height.
Step 1: Find height.
Given slant height: \[ l=13 \] Difference in radii: \[ R-r=18-6=12 \] Using Pythagoras: \[ l^2=h^2+(R-r)^2 \] \[ 13^2=h^2+12^2 \] \[ 169=h^2+144 \] \[ h^2=25 \] \[ h=5 \]
Step 2: Substitute in volume formula.
\[ V=\frac13\pi (5)(18^2+6^2+18\times6) \] \[ =\frac53\pi (324+36+108) \] \[ =\frac53\pi (468) \] \[ =5\pi(156) \] \[ =780\pi \] Thus, the volume of the frustum is: \[ \boxed{780\pi} \]
Step 1: Find height.
Given slant height: \[ l=13 \] Difference in radii: \[ R-r=18-6=12 \] Using Pythagoras: \[ l^2=h^2+(R-r)^2 \] \[ 13^2=h^2+12^2 \] \[ 169=h^2+144 \] \[ h^2=25 \] \[ h=5 \]
Step 2: Substitute in volume formula.
\[ V=\frac13\pi (5)(18^2+6^2+18\times6) \] \[ =\frac53\pi (324+36+108) \] \[ =\frac53\pi (468) \] \[ =5\pi(156) \] \[ =780\pi \] Thus, the volume of the frustum is: \[ \boxed{780\pi} \]
Was this answer helpful?
0
0
Top TG ICET Mathematical Ability Questions
- \[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]
- \[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]
- If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
- The ratio of milk and water in a can of 36 liters is \(3:1\). If 6 more liters of water is added, then the ratio of the milk and water will be:
- If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]
View More Questions
Top TG ICET Geometry Questions
- The least number of square tiles required to cover the floor of a room with dimensions \(24\) meters \(78\) cm \(\times\) \(27\) meters \(26\) cm is:
- What is the area of a rhombus (in sq.m.) whose perimeter is 40 m and one of its diagonals is 16 m?
- The dimensions of a brick and a wall are \(20\text{ cm} \times 10\text{ cm} \times 7.5\text{ cm}\) and \(25\text{ m} \times 2\text{ m} \times 0.75\text{ m}\) respectively. How many bricks (in thousands) are required to construct the wall?
- The volume of a cuboid is twice that of the volume of a cube. The dimensions of the cuboid are 9 cm, 8 cm, and 6 cm. If it costs ₹2.50 per sq.cm. for painting, the amount required to paint the surfaces of the cube (in rupees) is:
- The length and height of a godown are \(22\)m and \(6.5\)m respectively. If the area of four walls is \(442\) sq.m., then the breadth of the room in meters is:
View More Questions
Top TG ICET Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions