(i) Radius of 1 solid iron sphere = r
Volume of 1 solid iron sphere = \(\frac{4}{3}\pi\)r3
Volume of 27 solid iron spheres =27 × [\(\frac{4}{3}\pi\)r3]
27 solid iron spheres are melted to form 1 iron sphere.
Therefore, the volume of this iron sphere will be equal to the volume of 27 solid iron spheres.
Let the radius of this new sphere be r'.
Volume of new solid iron sphere = \(\frac{4}{3}\pi\)r3
(\(\frac{4}{3}\)) \(\pi\)r'3 = 36\(\pi\)r3
\(⇒\) r'3 = 36\(\pi\)r³ ×\( \frac{3}{4}\pi\)
\(⇒\) r'3 = 27r³
\(⇒\) r' = \(^3\sqrt{27}\) r³
r' = 3r
Radius of the new sphere, r' = 3r
(ii) Surface area of 1 solid iron sphere of radius r =\( 4\pi r^2 \)
Surface area of iron sphere of radius r' = 4\(\pi\) (r')2
= 4 \(\pi\) (3r)2
= 36 \(\pi r^2\)
\(\frac{S}{S’}\) = \(\frac{4\pi r^2}{36\pi r^2} = \frac{1}{9}=1:9.\)
List-I | List-II | ||
(A) | Volume of cone | (I) | \(\frac{1}{3}\pi h(r_1^2+r_2^2+r_1r_2)\) |
(B) | Volume of sphere | (II) | \(\frac{1}{3}\pi r^2h\) |
(C) | Volume of Frustum | (III) | \(\pi r^2h\) |
(D) | Volume of cylinder | (IV) | \(\frac{4}{3}\pi r^3\) |
Use these adverbs to fill in the blanks in the sentences below.
awfully sorrowfully completely loftily carefully differently quickly nonchalantly
(i) The report must be read ________ so that performance can be improved.
(ii) At the interview, Sameer answered our questions _________, shrugging his shoulders.
(iii) We all behave _________ when we are tired or hungry.
(iv) The teacher shook her head ________ when Ravi lied to her.
(v) I ________ forgot about it.
(vi) When I complimented Revathi on her success, she just smiled ________ and turned away.
(vii) The President of the Company is ________ busy and will not be able to meet you.
(viii) I finished my work ________ so that I could go out to play