A box with no top has a height that is six times its length and a width that is 2 3 of its height. If the surface area is 576 cm 2 , find the dimensions of the box.

Given that: A box with no top has a height that is six times its length and a width that is 2 3 of its height. If the surface area is 576 cm 2 , We have to find the dimensions of the box. Here, h = 6 l , b = 4 l . . . . . 1 , where l , b , h are the dimensions of the box We know that, Surface area of open box = 2 l h + b h + l b So, 2 l 6 l + 4 l 6 l + l 4 l = 576 ⇒ 64 l 2 = 576 ⇒ l 2 = 9 ⇒ l = 3 From equation 1 , we get b = 12 c m , h = 18 c m Hence, its dimensions are l = 3 c m , b = 12 c m & h = 18 c m

E M B I B E

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 3>Q 2

HARD

MYP:4-5

IMPORTANT

Earn 100

The square base of the Great pyramid at Giza measures $230.4$ m on each side. Its slant height is $186.4$ m.

Determine the ratio of the height of the pyramid to the perimeter of its base.

Important Questions on Problem-Solving

HARD

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 3>Q 2

The square base of the Great pyramid at Giza measures 230.4m on each side. Its slant height is 186.4 m.

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Explain how this ratio is related to the number $π$ .

HARD

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 3>Q 2

The square base of the Great pyramid at Giza measures $230.4 m$ on each side. Its slant height is $186.4 m$ .

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Discuss whether you think this is a coincidence.

HARD

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 4>Q 1

The height of a cylinder is twice as long as its diameter. Its volume is

500 {cm}^{3}

. Find the area of its base.

MEDIUM

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 4>Q 2

The diagonal of a cube (that passes through the middle of the cube, as shown in the diagram at right) measures $17.32 cm$ . Find the volume of the cube.

Question Image

MEDIUM

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 4>Q 3

A box with no top has a height that is six times its length and a width that is

\frac{2}{3}

of its height. If the surface area is

576 {cm}^{2}

, find the dimensions of the box.

MEDIUM

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 4>Q 4

When milk freezes, its volume increases by one-fifteenth. Find the fraction by which its volume will decrease when it melts back into a liquid state.

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MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 4>Q 5

It takes Nathan twice as long mow the lawn with the pushmower than with the electric mower. One day, he used the electric mower for $30$ minutes. Then it broke down. He took $20$ minutes the lawn with the pushmower finish mowing. Find how long it takes Nathan to mow the whole lawn using only the electric mower.

MEDIUM

MYP:4-5

IMPORTANT

MYP Mathematics A concept based approach 4&5 Standard>Chapter 1 - Problem-Solving>Practice 4>Q 6

The surface area of a cube-shaped box without a top is $252 {cm}^{2}$ . Find the volume of the box.