A cube has all its edges 7 cm long. 5 of it's 6 faces are painted while one face is left unpainted. Once the paint dries, the cube is then cut into smaller cubes of dimensions 1 cm x 1cm x 1cm for each small cube. Thus 343 new smaller cubes are formed.
Now answer the next 3 questions based on this data .
(1) How many smaller cubes will have 2 of their faces painted and remaining 4 faces unpainted ?
(2)How many smaller cubes will have 1 of their faces painted and remaining 5 faces unpainted ?
(3)How many smaller cubes will have none of their faces painted ?
Please answer it step by step !!
Answers
A cube has all its edges 7 cm long. 5 of it's 6 faces are painted while one face is left unpainted. Once the paint dries, the cube is then cut into smaller cubes of dimensions 1 cm x 1cm x 1cm for each small cube. Thus 343 new smaller cubes are formed.
A cube has all its edges 7 cm long. 5 of it's 6 faces are painted while one face is left unpainted. Once the paint dries, the cube is then cut into smaller cubes of dimensions 1 cm x 1cm x 1cm for each small cube. Thus 343 new smaller cubes are formed. Now answer the next 3 questions based on this data .
A cube has all its edges 7 cm long. 5 of it's 6 faces are painted while one face is left unpainted. Once the paint dries, the cube is then cut into smaller cubes of dimensions 1 cm x 1cm x 1cm for each small cube. Thus 343 new smaller cubes are formed. Now answer the next 3 questions based on this data .(1) How many smaller cubes will have 2 of their faces painted and remaining 4 faces unpainted ?
A cube has all its edges 7 cm long. 5 of it's 6 faces are painted while one face is left unpainted. Once the paint dries, the cube is then cut into smaller cubes of dimensions 1 cm x 1cm x 1cm for each small cube. Thus 343 new smaller cubes are formed. Now answer the next 3 questions based on this data .(1) How many smaller cubes will have 2 of their faces painted and remaining 4 faces unpainted ?(2)How many smaller cubes will have 1 of their faces painted and remaining 5 faces unpainted ?
A cube has all its edges 7 cm long. 5 of it's 6 faces are painted while one face is left unpainted. Once the paint dries, the cube is then cut into smaller cubes of dimensions 1 cm x 1cm x 1cm for each small cube. Thus 343 new smaller cubes are formed. Now answer the next 3 questions based on this data .(1) How many smaller cubes will have 2 of their faces painted and remaining 4 faces unpainted ?(2)How many smaller cubes will have 1 of their faces painted and remaining 5 faces unpainted ? (3)How many smaller cubes will have none of their faces painted ?
A cube has all its edges 7 cm long. 5 of it's 6 faces are painted while one face is left unpainted. Once the paint dries, the cube is then cut into smaller cubes of dimensions 1 cm x 1cm x 1cm for each small cube. Thus 343 new smaller cubes are formed. Now answer the next 3 questions based on this data .(1) How many smaller cubes will have 2 of their faces painted and remaining 4 faces unpainted ?(2)How many smaller cubes will have 1 of their faces painted and remaining 5 faces unpainted ? (3)How many smaller cubes will have none of their faces painted ?Please answer it step by step !!
A cube has all its edges 7 cm long. 5 of it's 6 faces are painted while one face is left unpainted. Once the paint dries, the cube is then cut into smaller cubes of dimensions 1 cm x 1cm x 1cm for each small cube. Thus 343 new smaller cubes are formed. Now answer the next 3 questions based on this data .(1) How many smaller cubes will have 2 of their faces painted and remaining 4 faces unpainted ?(2)How many smaller cubes will have 1 of their faces painted and remaining 5 faces unpainted ? (3)How many smaller cubes will have none of their faces painted ?Please answer it step by step !!
Answer:
sinθ+cosθ=a
secθ+cscθ=b
\sf\underline \red{ To\:Find}
ToFind
We have to find the value of b(a²-1)
\sf\underline \pink{ Solution }
Solution
By putting the given values
\begin{gathered}:\implies\sf\ \ b(a^2-1)\\ \\ \\ :\implies\sf\ \ sec\theta+csc\theta\big\{(sin\theta+cos\theta)^2-1)\big\}\\ \\ \\ \bullet\sf\ sec\theta=\dfrac{1}{cos\theta}\ \ ;\ csc\theta=\dfrac{1}{sin\theta}\\ \\ \\ :\implies\sf\ \dfrac{1}{cos\theta}+\dfrac{1}{sin\theta}\big\{sin^2\theta+cos^2\theta+2sin\theta cos\theta-1\big\}\\ \\ \\ \bullet\sf\ \ sin^2\theta+cos^2\theta=1\\ \\ \\ :\implies\sf\dfrac{sin\theta+cos\theta}{sin\theta\ cos\theta}\big\{\cancel{1}+2sin\theta\ cos\theta \cancel{-1}\big\}\\ \\ \\ :\implies\sf\ \dfrac{sin\theta+cos\theta}{\cancel{sin\theta cos\theta}}\times 2\cancel{sin\theta cos\theta}\\ \\ \\ :\implies\sf\ \ 2(sin\theta+cos\theta)\end{gathered}
:⟹ b(a
2
−1)
:⟹ secθ+cscθ{(sinθ+cosθ)
2
−1)}
∙ secθ=
cosθ
1
; cscθ=
sinθ
1
:⟹
cosθ
1
+
sinθ
1
{sin
2
θ+cos
2
θ+2sinθcosθ−1}
∙ sin
2
θ+cos
2
θ=1
:⟹
sinθ cosθ
sinθ+cosθ
{
1
+2sinθ cosθ
−1
}
:⟹
sinθcosθ
sinθ+cosθ
×2
sinθcosθ
:⟹ 2(sinθ+cosθ)
\underline{\bigstar{\blue{\sf\ \ b(a^2-1)= 2(sin\theta+cos\theta)}}}
★ b(a
2
−1)=2(sinθ+cosθ