An ice cream cone full of ice cream has a rad | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The ice cream cone is a combination of a hemisphere and a cone.Given,radius of the hemisphere $(r)$ $= 5 \, cm$.Volume of the hemisphere $= \frac{

Vedclass · Accepted Answer

$327.4$

Vedclass · Answer

(D) The ice cream cone is a combination of a hemisphere and a cone.Given,radius of the hemisphere $(r)$ $= 5 \, cm$.Volume of the hemisphere $= \frac{2}{3} \pi r^{3} = \frac{2}{3} 	imes \frac{22}{7} 	imes (5)^{3} = \frac{5500}{21} \approx 261.90 \, cm^{3}$.Now,the radius of the cone $(r)$ $= 5 \, cm$.The total height of the ice cream cone is $10 \, cm$. Since the hemisphere has a radius of $5 \, cm$,the height of the conical part $(h)$ $= 10 - 5 = 5 \, cm$.Volume of the cone $= \frac{1}{3} \pi r^{2} h = \frac{1}{3} 	imes \frac{22}{7} 	imes (5)^{2} 	imes 5 = \frac{2750}{21} \approx 130.95 \, cm^{3}$.Total volume of the ice cream cone $= 261.90 + 130.95 = 392.85 \, cm^{3}$.Since $\frac{1}{6}$ part is left unfilled,the volume of ice cream filled is $\frac{5}{6}$ of the total volume.Required volume of ice cream $= \frac{5}{6} 	imes 392.85 = 5 	imes 65.475 = 327.375 \approx 327.4 \, cm^{3}$.

Part $I$	Part $II$
$1.$ $CSA$ of a cylinder	$a.$ $3\pi r^2$
$2.$ $CSA$ of a sphere	$b.$ $2\pi rh$
$3.$ $CSA$ of a cone	$c.$ $4\pi r^2$
$4.$ $TSA$ of a hemisphere	$d.$ $\pi rl$

An ice cream cone full of ice cream has a radius of $5 \, cm$ and a total height of $10 \, cm$ as shown in the figure. Calculate the volume of the ice cream,provided that its $\frac{1}{6}$ part is left unfilled with ice cream. (in $cm^{3}$)

Similar Questions

The volume of a $1-$ rupee coin is given by the formula $\ldots \ldots \ldots . . .$

$A$ hemispherical bowl of internal radius $9 \,cm$ is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius $1.5 \,cm$ and height $4 \,cm$. How many bottles are needed to empty the bowl?

$A$ cone of maximum size is carved out from a cube of edge $14 \, cm$. Find the surface area of the cone and the surface area of the remaining solid left after the cone is carved out.

Which of the following correctly matches the information given in Part $I$ and Part $II$?

Part $I$ Part $II$

$1.$ $CSA$ of a cylinder $a.$ $3\pi r^2$

$2.$ $CSA$ of a sphere $b.$ $2\pi rh$

$3.$ $CSA$ of a cone $c.$ $4\pi r^2$

$4.$ $TSA$ of a hemisphere $d.$ $\pi rl$

$1 \, m^3 = \dots \text{liters}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module