When a right triangle of area 3 is rotated 360^ about its shorter… - Vidyadip

MCQ

When a right triangle of area $3$ is rotated $360^\circ $ about its shorter leg, the solid that results has a volume of $30$. Calculate the volume of the solid if the same right triangle is rotated about its longer leg.

A
$0.99$
✓
$7.90$
C
$8.88$
D
$31.42$

✓

Answer

Correct option: B.

$7.90$

Let the length of shorter leg be hh, length of longer leg be $k$, volume of resulting solid is $30$.
The resulting solid is cone, so volume is $\frac{1}{3}\times\pi\text{k}^2\text{h}=30$
Area of triangle is $\frac{1}{2}\times\text{h}\text{k}=3,$ which implies $hk = 6$
which gives $\frac{1}{3}\times\pi6\text{k}=30,$ $\text{k}=\frac{15}{\pi}$
Volume when rotated with longer leg is
$\frac{1}{3}\times\pi\text{h}^2\text{k}=2\pi\text{h}$
$=\frac{2\pi6}{\text{k}}=\frac{12\pi}{15}\times\pi=7.9$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q. [1 Marks Each]" from Symmetry→Symmetry — all question types→MATHS STD 7 question papers→Gujarat Board STD 7 question papers→Gujarat Board question paper generator→

Similar questions

$\frac{-3}{14} \times ?=\frac{5}{12}$

Which of the following products is not equal to 1 ?

The circumferences of two circles are in the ratio $3: 4$. The ratio of their areas is

In Fig. $\angle\text{AOC}$ and $\angle\text{BOC}$ form a pair of:

Mark $(\checkmark)$ against the correct answer in the following: $78\frac{3}{4}\div2\frac{1}{2}=?$

Mark against the correct answer in the following:
$6$ dozen eggs are bought for $Rs. 108$. How much will $132$ eggs cost ?

Mark $(\checkmark)$ against the correct answer in the following:
$0.5 \times 0.05 = ?$

If $x\%$ of $75$ is $12$, then $x =$

The value of the root $ \sqrt{\frac{16}{36}+\frac{1}{4}}$ is:

A survey of $40$ children showed that $25\%$ liked playing football. How many children liked playing football?