Đường kính của một hình cầu bằng cạnh của một hình lập phương. Thể tích của hình lập phương gấp thể tích hình cầu:

Cho hình chóp S.ABCD có đáy ABCD là hình vuông cạnh a, SA vuông góc với mặt phẳng (ABCD), góc giữa đường thẳng SC và mặt phẳng (ABCD) bằng ${{45}^{0}}$. Tính khoảng cách giữa hai đường thẳng SB, AC.

Cho hình chóp S.ABC có $SA=SB=SC=1$, $ASB={{90}^{0}}$, $BSC={{120}^{0}}$, $CSA={{90}^{0}}$. Tính theo a thể tích khối chóp S.ABC

Hình cóp S.ABC có đáy ABC là tam giác vuông cân ($BA=BC$), cạnh bên SA vuông góc với mặt phẳng đáy và có độ dài là $a\sqrt{3}$, cạnh bên SB tạo với đáy một góc ${{60}^{0}}$. Tính diện tích toàn phần của hình chóp

Cho hình chóp S.ABCD có thể tích bằng 48 và ABCD là hình thoi. Các điểm M, N, P, Q lần lượt là các điểm trên các đoạn SA, SB, SC, SD thỏa mãn: $SA=2SM;SB=3SN;SC=4SP;SD=5SQ$. Tính thể tích khối chóp S.MNPQ?

A person spends 33000 vnd to buy 10 chicken eggs and 5 duck eggs. Find the price of one chicken egg and the price of one duck egg ? Such that the price of 5 chicken eggs is 7500 vnd more than the price of two duck eggs .

An and Hung have 82000vnd. After An buys $\frac{4}{7}$ of her money and Hung buys $\frac{2}{5}$ of his money, the remaining money of Hung is 6000 more than An. Find An’s money at first ?

Find X; Y; Z such that : $\frac{X-1}{2}=\frac{Y-2}{3}=\frac{Z-3}{4}$ và 2 x X  + 3 x Y – z = 50

Find X such that X + Y + Z = 350 và $\frac{6}{7}\times X=\frac{9}{11}\times Y=\frac{2}{3}\times Z$

There are three classes, they plant 230 trees totally. Such that if class 4A plants 3 trees, class 4B plants 2 trees and if class 4B plants 3 trees, class 4C plants 4 trees. How many tree does class 4C plant ?

In the garden, they plant 120 trees totally, consist of orange, lemon and mango. Such that the number of oranges is $\frac{2}{3}$ the number of lemons and mangos, the number of manges is $\frac{1}{5}$ the number of lemons and oranges. How many lemons are there ?

Hue , Hang and Mai go to plant tree. Such that the sum of trees of three person plant is 17 trees. The number of trees of Hue and Hang is three trees more than Mai. The number of trees of Hue is $\frac{2}{3}$ the number of trees of Hang. How many trees does Mai plant ?

Two man divide 425000 vnd each other. After the first man spends $\frac{1}{6}$ of his money, the second man spends $\frac{1}{7}$ of his money, the second man is 60 000 vnd more than the first man. How many moneys does the first man have ? ( vnd )

Given the expression : A = $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{n}$ . Such that : A = $\frac{49}{50}$ . Find the value of n ?

A store buys 200 both crab and frog. Such that the number leg of crab is 180 more than the number leg of frog. How many frogs are there ( counting that nipper of crab as leg of crab ) ?

There are 145 cents with denomination 5000vnd, 2000vnd and 1000vnd. The value of 145 cents is 312 000 vnd. The number of cent with denomination 2000vnd is 2 times the number of cent with denomination 1000vnd. How many cents with denomination 5000vnd are there ?

A person made some of product.The first day sold $\frac{3}{7}$ of product, if the price is 18000 vnd/product , the interest rate is 54 000vnd. The second day sold $\frac{2}{3}$ of the remaining product, if the price is 20000 vnd/product, the interest rate is 80 000 vnd. Find the sum of product is sold ?

The sum of two consecutive numbers is 3 times the difference of them and is a half the product of them. Find the greater number ?

The sum of chickens and ducks is 148. The product of them is 4747. Find the number of chicken ? ( Such that the number of chicken is more than the number of duck )

Find the greater such that the product of two numbers is 540 and the greater is $\frac{5}{3}$ the smaller ?

The area of a rectangle is 1372 m². Such that the width is $\frac{4}{7}$the length. Find the perimeter of the rectangle ? ( m )

Toan Aunt buys five tables and 7 chairs with the total cost is 3 010 000 vnd. The price of a table is 170 000 vnd more than the price of a chair. If  buying one table and 2 chairs, how much is it totally ? (vnd )

There are 5 natural numbers. If you add five numbers together and then the result divided by 5, the quotient is 138. To arrange in order of increasing. Then hen adding three fist number together and divided by 3, the quotient is 127. If adding three last number and divided by 3, the quotient is 148. What is the number in the middle ?

An has four stamps with type 1000vnd and three stamps type 2000vnd. Using one or many different stamps with the following value. How many ways does An have to pay money by sticking stamp on the envelope ?

Three chickens and two ducks weigh 32 kilograms ; four chikens and 3 ducks weigh 44 kilogram. The chickens have the same weigh and the ducks have the same weight. How much do two chickens and one duck weigh ?